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Simplifying (2x + -5)(2x + -5) = 11 Reorder the terms: (-5 + 2x)(2x + -5) = 11 Reorder the terms: (-5 + 2x)(-5 + 2x) = 11 Multiply (-5 + 2x) * (-5 + 2x) (-5(-5 + 2x) + 2x * (-5 + 2x)) = 11 ((-5 * -5 + 2x * -5) + 2x * (-5 + 2x)) = 11 ((25 + -10x) + 2x * (-5 + 2x)) = 11 (25 + -10x + (-5 * 2x + 2x * 2x)) = 11 (25 + -10x + (-10x + 4x2)) = 11 Combine like terms: -10x + -10x = -20x (25 + -20x + 4x2) = 11 Solving 25 + -20x + 4x2 = 11 Solving for variable 'x'. Reorder the terms: 25 + -11 + -20x + 4x2 = 11 + -11 Combine like terms: 25 + -11 = 14 14 + -20x + 4x2 = 11 + -11 Combine like terms: 11 + -11 = 0 14 + -20x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(7 + -10x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + -10x + 2x2)' equal to zero and attempt to solve: Simplifying 7 + -10x + 2x2 = 0 Solving 7 + -10x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3.5 + -5x + x2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + -5x + -3.5 + x2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + -5x + x2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + -5x + x2 = 0 + -3.5 -5x + x2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 -5x + x2 = -3.5 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -3.5 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -3.5 + 6.25 Combine like terms: -3.5 + 6.25 = 2.75 6.25 + -5x + x2 = 2.75 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 2.75 Calculate the square root of the right side: 1.658312395 Break this problem into two subproblems by setting (x + -2.5) equal to 1.658312395 and -1.658312395.Subproblem 1
x + -2.5 = 1.658312395 Simplifying x + -2.5 = 1.658312395 Reorder the terms: -2.5 + x = 1.658312395 Solving -2.5 + x = 1.658312395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 1.658312395 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 1.658312395 + 2.5 x = 1.658312395 + 2.5 Combine like terms: 1.658312395 + 2.5 = 4.158312395 x = 4.158312395 Simplifying x = 4.158312395Subproblem 2
x + -2.5 = -1.658312395 Simplifying x + -2.5 = -1.658312395 Reorder the terms: -2.5 + x = -1.658312395 Solving -2.5 + x = -1.658312395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -1.658312395 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -1.658312395 + 2.5 x = -1.658312395 + 2.5 Combine like terms: -1.658312395 + 2.5 = 0.841687605 x = 0.841687605 Simplifying x = 0.841687605Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.158312395, 0.841687605}Solution
x = {4.158312395, 0.841687605}
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