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Simplifying -16x2 + 110x + 5 = 135 Reorder the terms: 5 + 110x + -16x2 = 135 Solving 5 + 110x + -16x2 = 135 Solving for variable 'x'. Reorder the terms: 5 + -135 + 110x + -16x2 = 135 + -135 Combine like terms: 5 + -135 = -130 -130 + 110x + -16x2 = 135 + -135 Combine like terms: 135 + -135 = 0 -130 + 110x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-65 + 55x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-65 + 55x + -8x2)' equal to zero and attempt to solve: Simplifying -65 + 55x + -8x2 = 0 Solving -65 + 55x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 8.125 + -6.875x + x2 = 0 Move the constant term to the right: Add '-8.125' to each side of the equation. 8.125 + -6.875x + -8.125 + x2 = 0 + -8.125 Reorder the terms: 8.125 + -8.125 + -6.875x + x2 = 0 + -8.125 Combine like terms: 8.125 + -8.125 = 0.000 0.000 + -6.875x + x2 = 0 + -8.125 -6.875x + x2 = 0 + -8.125 Combine like terms: 0 + -8.125 = -8.125 -6.875x + x2 = -8.125 The x term is -6.875x. Take half its coefficient (-3.4375). Square it (11.81640625) and add it to both sides. Add '11.81640625' to each side of the equation. -6.875x + 11.81640625 + x2 = -8.125 + 11.81640625 Reorder the terms: 11.81640625 + -6.875x + x2 = -8.125 + 11.81640625 Combine like terms: -8.125 + 11.81640625 = 3.69140625 11.81640625 + -6.875x + x2 = 3.69140625 Factor a perfect square on the left side: (x + -3.4375)(x + -3.4375) = 3.69140625 Calculate the square root of the right side: 1.921303269 Break this problem into two subproblems by setting (x + -3.4375) equal to 1.921303269 and -1.921303269.Subproblem 1
x + -3.4375 = 1.921303269 Simplifying x + -3.4375 = 1.921303269 Reorder the terms: -3.4375 + x = 1.921303269 Solving -3.4375 + x = 1.921303269 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.4375' to each side of the equation. -3.4375 + 3.4375 + x = 1.921303269 + 3.4375 Combine like terms: -3.4375 + 3.4375 = 0.0000 0.0000 + x = 1.921303269 + 3.4375 x = 1.921303269 + 3.4375 Combine like terms: 1.921303269 + 3.4375 = 5.358803269 x = 5.358803269 Simplifying x = 5.358803269Subproblem 2
x + -3.4375 = -1.921303269 Simplifying x + -3.4375 = -1.921303269 Reorder the terms: -3.4375 + x = -1.921303269 Solving -3.4375 + x = -1.921303269 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.4375' to each side of the equation. -3.4375 + 3.4375 + x = -1.921303269 + 3.4375 Combine like terms: -3.4375 + 3.4375 = 0.0000 0.0000 + x = -1.921303269 + 3.4375 x = -1.921303269 + 3.4375 Combine like terms: -1.921303269 + 3.4375 = 1.516196731 x = 1.516196731 Simplifying x = 1.516196731Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.358803269, 1.516196731}Solution
x = {5.358803269, 1.516196731}
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