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Simplifying -5x2 + 40x + -78 = 0 Reorder the terms: -78 + 40x + -5x2 = 0 Solving -78 + 40x + -5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 15.6 + -8x + x2 = 0 Move the constant term to the right: Add '-15.6' to each side of the equation. 15.6 + -8x + -15.6 + x2 = 0 + -15.6 Reorder the terms: 15.6 + -15.6 + -8x + x2 = 0 + -15.6 Combine like terms: 15.6 + -15.6 = 0.0 0.0 + -8x + x2 = 0 + -15.6 -8x + x2 = 0 + -15.6 Combine like terms: 0 + -15.6 = -15.6 -8x + x2 = -15.6 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -15.6 + 16 Reorder the terms: 16 + -8x + x2 = -15.6 + 16 Combine like terms: -15.6 + 16 = 0.4 16 + -8x + x2 = 0.4 Factor a perfect square on the left side: (x + -4)(x + -4) = 0.4 Calculate the square root of the right side: 0.632455532 Break this problem into two subproblems by setting (x + -4) equal to 0.632455532 and -0.632455532.Subproblem 1
x + -4 = 0.632455532 Simplifying x + -4 = 0.632455532 Reorder the terms: -4 + x = 0.632455532 Solving -4 + x = 0.632455532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 0.632455532 + 4 Combine like terms: -4 + 4 = 0 0 + x = 0.632455532 + 4 x = 0.632455532 + 4 Combine like terms: 0.632455532 + 4 = 4.632455532 x = 4.632455532 Simplifying x = 4.632455532Subproblem 2
x + -4 = -0.632455532 Simplifying x + -4 = -0.632455532 Reorder the terms: -4 + x = -0.632455532 Solving -4 + x = -0.632455532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -0.632455532 + 4 Combine like terms: -4 + 4 = 0 0 + x = -0.632455532 + 4 x = -0.632455532 + 4 Combine like terms: -0.632455532 + 4 = 3.367544468 x = 3.367544468 Simplifying x = 3.367544468Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.632455532, 3.367544468}
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