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Simplifying -16x2 + 40x + 104.64 = 0 Reorder the terms: 104.64 + 40x + -16x2 = 0 Solving 104.64 + 40x + -16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -6.54 + -2.5x + x2 = 0 Move the constant term to the right: Add '6.54' to each side of the equation. -6.54 + -2.5x + 6.54 + x2 = 0 + 6.54 Reorder the terms: -6.54 + 6.54 + -2.5x + x2 = 0 + 6.54 Combine like terms: -6.54 + 6.54 = 0.00 0.00 + -2.5x + x2 = 0 + 6.54 -2.5x + x2 = 0 + 6.54 Combine like terms: 0 + 6.54 = 6.54 -2.5x + x2 = 6.54 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 6.54 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 6.54 + 1.5625 Combine like terms: 6.54 + 1.5625 = 8.1025 1.5625 + -2.5x + x2 = 8.1025 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 8.1025 Calculate the square root of the right side: 2.846489065 Break this problem into two subproblems by setting (x + -1.25) equal to 2.846489065 and -2.846489065.Subproblem 1
x + -1.25 = 2.846489065 Simplifying x + -1.25 = 2.846489065 Reorder the terms: -1.25 + x = 2.846489065 Solving -1.25 + x = 2.846489065 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 2.846489065 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 2.846489065 + 1.25 x = 2.846489065 + 1.25 Combine like terms: 2.846489065 + 1.25 = 4.096489065 x = 4.096489065 Simplifying x = 4.096489065Subproblem 2
x + -1.25 = -2.846489065 Simplifying x + -1.25 = -2.846489065 Reorder the terms: -1.25 + x = -2.846489065 Solving -1.25 + x = -2.846489065 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -2.846489065 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -2.846489065 + 1.25 x = -2.846489065 + 1.25 Combine like terms: -2.846489065 + 1.25 = -1.596489065 x = -1.596489065 Simplifying x = -1.596489065Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.096489065, -1.596489065}
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