The problem is to solve the quadratic equation $7x^2 + 42x - 49 = 0$ by factoring.

AlgebraQuadratic EquationsFactoringEquation Solving
2025/6/4

1. Problem Description

The problem is to solve the quadratic equation 7x2+42x49=07x^2 + 42x - 49 = 0 by factoring.

2. Solution Steps

First, we can divide the entire equation by 7 to simplify it:
x2+6x7=0x^2 + 6x - 7 = 0
Now, we need to factor the quadratic expression x2+6x7x^2 + 6x - 7. We are looking for two numbers that multiply to -7 and add up to

6. These numbers are 7 and -

1. So, we can factor the quadratic expression as $(x + 7)(x - 1)$.

Thus, the equation becomes (x+7)(x1)=0(x + 7)(x - 1) = 0.
Now, we set each factor equal to zero and solve for xx:
x+7=0x + 7 = 0 or x1=0x - 1 = 0
x=7x = -7 or x=1x = 1

3. Final Answer

The solutions are x=7x = -7 and x=1x = 1.

Related problems in "Algebra"

We are asked to evaluate the expression $A = 2025^3 - 2024 \cdot 2025^2 - 2024^2 \cdot 2025 + 2024^3...

PolynomialsFactoringAlgebraic ManipulationSimplification
2025/8/5

Given that $log_{10}5 \approx 0.699$, find the value of $log_{10}25$.

LogarithmsLogarithm PropertiesApproximation
2025/8/4

The image presents two math problems: Problem 4: Simplify the expression $\frac{3 \times 10^2}{5 \ti...

Scientific NotationExponentsSimplification
2025/8/4

The problem consists of two parts: (a) Simplify the expression $\frac{2x - 3}{x^2 - 9} + \frac{4}{x ...

Algebraic ExpressionsSimplificationExponentsEquations
2025/8/4

Problem 5: If some soy sauce is used, the remainder is $\frac{3}{8}$ L. This amount is $\frac{1}{6}$...

Word ProblemsFractionsEquationsAreaRectangles
2025/8/4

The image shows the quadratic formula, $x = \frac{-b \pm \sqrt{D}}{2a}$, and the statement "If $D < ...

Quadratic EquationsDiscriminantComplex NumbersRoots of Equations
2025/8/3

The problem asks to solve for $x$ in the following two quadratic equations: a) $x^2 - 2x - 2 = 0$ b)...

Quadratic EquationsQuadratic FormulaRoots
2025/8/3

The problem asks us to factorize the given expressions completely.

FactorizationAlgebraic Expressions
2025/8/1

The problem is to factorize a list of given algebraic expressions completely.

FactorizationAlgebraic ExpressionsCommon Factors
2025/8/1

The problem consists of five sub-problems related to standard form. 1. Express 450,000 in standard ...

Scientific NotationExponentsNumber Representation
2025/8/1