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Simplifying 5(x + -2)(x + -2) + -40 = 80 Reorder the terms: 5(-2 + x)(x + -2) + -40 = 80 Reorder the terms: 5(-2 + x)(-2 + x) + -40 = 80 Multiply (-2 + x) * (-2 + x) 5(-2(-2 + x) + x(-2 + x)) + -40 = 80 5((-2 * -2 + x * -2) + x(-2 + x)) + -40 = 80 5((4 + -2x) + x(-2 + x)) + -40 = 80 5(4 + -2x + (-2 * x + x * x)) + -40 = 80 5(4 + -2x + (-2x + x2)) + -40 = 80 Combine like terms: -2x + -2x = -4x 5(4 + -4x + x2) + -40 = 80 (4 * 5 + -4x * 5 + x2 * 5) + -40 = 80 (20 + -20x + 5x2) + -40 = 80 Reorder the terms: 20 + -40 + -20x + 5x2 = 80 Combine like terms: 20 + -40 = -20 -20 + -20x + 5x2 = 80 Solving -20 + -20x + 5x2 = 80 Solving for variable 'x'. Reorder the terms: -20 + -80 + -20x + 5x2 = 80 + -80 Combine like terms: -20 + -80 = -100 -100 + -20x + 5x2 = 80 + -80 Combine like terms: 80 + -80 = 0 -100 + -20x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-20 + -4x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-20 + -4x + x2)' equal to zero and attempt to solve: Simplifying -20 + -4x + x2 = 0 Solving -20 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + -4x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + -4x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -4x + x2 = 0 + 20 -4x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 -4x + x2 = 20 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 20 + 4 Reorder the terms: 4 + -4x + x2 = 20 + 4 Combine like terms: 20 + 4 = 24 4 + -4x + x2 = 24 Factor a perfect square on the left side: (x + -2)(x + -2) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (x + -2) equal to 4.898979486 and -4.898979486.Subproblem 1
x + -2 = 4.898979486 Simplifying x + -2 = 4.898979486 Reorder the terms: -2 + x = 4.898979486 Solving -2 + x = 4.898979486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 4.898979486 + 2 Combine like terms: -2 + 2 = 0 0 + x = 4.898979486 + 2 x = 4.898979486 + 2 Combine like terms: 4.898979486 + 2 = 6.898979486 x = 6.898979486 Simplifying x = 6.898979486Subproblem 2
x + -2 = -4.898979486 Simplifying x + -2 = -4.898979486 Reorder the terms: -2 + x = -4.898979486 Solving -2 + x = -4.898979486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -4.898979486 + 2 Combine like terms: -2 + 2 = 0 0 + x = -4.898979486 + 2 x = -4.898979486 + 2 Combine like terms: -4.898979486 + 2 = -2.898979486 x = -2.898979486 Simplifying x = -2.898979486Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.898979486, -2.898979486}Solution
x = {6.898979486, -2.898979486}
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