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Simplifying (2x + -5)(2x + -5) + -11(4x + 3) = 2 Reorder the terms: (-5 + 2x)(2x + -5) + -11(4x + 3) = 2 Reorder the terms: (-5 + 2x)(-5 + 2x) + -11(4x + 3) = 2 Multiply (-5 + 2x) * (-5 + 2x) (-5(-5 + 2x) + 2x * (-5 + 2x)) + -11(4x + 3) = 2 ((-5 * -5 + 2x * -5) + 2x * (-5 + 2x)) + -11(4x + 3) = 2 ((25 + -10x) + 2x * (-5 + 2x)) + -11(4x + 3) = 2 (25 + -10x + (-5 * 2x + 2x * 2x)) + -11(4x + 3) = 2 (25 + -10x + (-10x + 4x2)) + -11(4x + 3) = 2 Combine like terms: -10x + -10x = -20x (25 + -20x + 4x2) + -11(4x + 3) = 2 Reorder the terms: 25 + -20x + 4x2 + -11(3 + 4x) = 2 25 + -20x + 4x2 + (3 * -11 + 4x * -11) = 2 25 + -20x + 4x2 + (-33 + -44x) = 2 Reorder the terms: 25 + -33 + -20x + -44x + 4x2 = 2 Combine like terms: 25 + -33 = -8 -8 + -20x + -44x + 4x2 = 2 Combine like terms: -20x + -44x = -64x -8 + -64x + 4x2 = 2 Solving -8 + -64x + 4x2 = 2 Solving for variable 'x'. Reorder the terms: -8 + -2 + -64x + 4x2 = 2 + -2 Combine like terms: -8 + -2 = -10 -10 + -64x + 4x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -10 + -64x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + -32x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -32x + 2x2)' equal to zero and attempt to solve: Simplifying -5 + -32x + 2x2 = 0 Solving -5 + -32x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.5 + -16x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -16x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -16x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -16x + x2 = 0 + 2.5 -16x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -16x + x2 = 2.5 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = 2.5 + 64 Reorder the terms: 64 + -16x + x2 = 2.5 + 64 Combine like terms: 2.5 + 64 = 66.5 64 + -16x + x2 = 66.5 Factor a perfect square on the left side: (x + -8)(x + -8) = 66.5 Calculate the square root of the right side: 8.154753215 Break this problem into two subproblems by setting (x + -8) equal to 8.154753215 and -8.154753215.Subproblem 1
x + -8 = 8.154753215 Simplifying x + -8 = 8.154753215 Reorder the terms: -8 + x = 8.154753215 Solving -8 + x = 8.154753215 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 8.154753215 + 8 Combine like terms: -8 + 8 = 0 0 + x = 8.154753215 + 8 x = 8.154753215 + 8 Combine like terms: 8.154753215 + 8 = 16.154753215 x = 16.154753215 Simplifying x = 16.154753215Subproblem 2
x + -8 = -8.154753215 Simplifying x + -8 = -8.154753215 Reorder the terms: -8 + x = -8.154753215 Solving -8 + x = -8.154753215 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -8.154753215 + 8 Combine like terms: -8 + 8 = 0 0 + x = -8.154753215 + 8 x = -8.154753215 + 8 Combine like terms: -8.154753215 + 8 = -0.154753215 x = -0.154753215 Simplifying x = -0.154753215Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.154753215, -0.154753215}Solution
x = {16.154753215, -0.154753215}
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