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Simplifying (2x + -10)(2x + -20) = 90 Reorder the terms: (-10 + 2x)(2x + -20) = 90 Reorder the terms: (-10 + 2x)(-20 + 2x) = 90 Multiply (-10 + 2x) * (-20 + 2x) (-10(-20 + 2x) + 2x * (-20 + 2x)) = 90 ((-20 * -10 + 2x * -10) + 2x * (-20 + 2x)) = 90 ((200 + -20x) + 2x * (-20 + 2x)) = 90 (200 + -20x + (-20 * 2x + 2x * 2x)) = 90 (200 + -20x + (-40x + 4x2)) = 90 Combine like terms: -20x + -40x = -60x (200 + -60x + 4x2) = 90 Solving 200 + -60x + 4x2 = 90 Solving for variable 'x'. Reorder the terms: 200 + -90 + -60x + 4x2 = 90 + -90 Combine like terms: 200 + -90 = 110 110 + -60x + 4x2 = 90 + -90 Combine like terms: 90 + -90 = 0 110 + -60x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(55 + -30x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(55 + -30x + 2x2)' equal to zero and attempt to solve: Simplifying 55 + -30x + 2x2 = 0 Solving 55 + -30x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 27.5 + -15x + x2 = 0 Move the constant term to the right: Add '-27.5' to each side of the equation. 27.5 + -15x + -27.5 + x2 = 0 + -27.5 Reorder the terms: 27.5 + -27.5 + -15x + x2 = 0 + -27.5 Combine like terms: 27.5 + -27.5 = 0.0 0.0 + -15x + x2 = 0 + -27.5 -15x + x2 = 0 + -27.5 Combine like terms: 0 + -27.5 = -27.5 -15x + x2 = -27.5 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = -27.5 + 56.25 Reorder the terms: 56.25 + -15x + x2 = -27.5 + 56.25 Combine like terms: -27.5 + 56.25 = 28.75 56.25 + -15x + x2 = 28.75 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 28.75 Calculate the square root of the right side: 5.361902647 Break this problem into two subproblems by setting (x + -7.5) equal to 5.361902647 and -5.361902647.Subproblem 1
x + -7.5 = 5.361902647 Simplifying x + -7.5 = 5.361902647 Reorder the terms: -7.5 + x = 5.361902647 Solving -7.5 + x = 5.361902647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 5.361902647 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 5.361902647 + 7.5 x = 5.361902647 + 7.5 Combine like terms: 5.361902647 + 7.5 = 12.861902647 x = 12.861902647 Simplifying x = 12.861902647Subproblem 2
x + -7.5 = -5.361902647 Simplifying x + -7.5 = -5.361902647 Reorder the terms: -7.5 + x = -5.361902647 Solving -7.5 + x = -5.361902647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -5.361902647 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -5.361902647 + 7.5 x = -5.361902647 + 7.5 Combine like terms: -5.361902647 + 7.5 = 2.138097353 x = 2.138097353 Simplifying x = 2.138097353Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.861902647, 2.138097353}Solution
x = {12.861902647, 2.138097353}
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