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Simplifying -3x2 + 78x = -45 Reorder the terms: 78x + -3x2 = -45 Solving 78x + -3x2 = -45 Solving for variable 'x'. Reorder the terms: 45 + 78x + -3x2 = -45 + 45 Combine like terms: -45 + 45 = 0 45 + 78x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(15 + 26x + -1x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(15 + 26x + -1x2)' equal to zero and attempt to solve: Simplifying 15 + 26x + -1x2 = 0 Solving 15 + 26x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -15 + -26x + x2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + -26x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + -26x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -26x + x2 = 0 + 15 -26x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 -26x + x2 = 15 The x term is -26x. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26x + 169 + x2 = 15 + 169 Reorder the terms: 169 + -26x + x2 = 15 + 169 Combine like terms: 15 + 169 = 184 169 + -26x + x2 = 184 Factor a perfect square on the left side: (x + -13)(x + -13) = 184 Calculate the square root of the right side: 13.564659966 Break this problem into two subproblems by setting (x + -13) equal to 13.564659966 and -13.564659966.Subproblem 1
x + -13 = 13.564659966 Simplifying x + -13 = 13.564659966 Reorder the terms: -13 + x = 13.564659966 Solving -13 + x = 13.564659966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = 13.564659966 + 13 Combine like terms: -13 + 13 = 0 0 + x = 13.564659966 + 13 x = 13.564659966 + 13 Combine like terms: 13.564659966 + 13 = 26.564659966 x = 26.564659966 Simplifying x = 26.564659966Subproblem 2
x + -13 = -13.564659966 Simplifying x + -13 = -13.564659966 Reorder the terms: -13 + x = -13.564659966 Solving -13 + x = -13.564659966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = -13.564659966 + 13 Combine like terms: -13 + 13 = 0 0 + x = -13.564659966 + 13 x = -13.564659966 + 13 Combine like terms: -13.564659966 + 13 = -0.564659966 x = -0.564659966 Simplifying x = -0.564659966Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.564659966, -0.564659966}Solution
x = {26.564659966, -0.564659966}
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