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Simplifying 5x2 + -40x + 56 = 0 Reorder the terms: 56 + -40x + 5x2 = 0 Solving 56 + -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'. 11.2 + -8x + x2 = 0 Move the constant term to the right: Add '-11.2' to each side of the equation. 11.2 + -8x + -11.2 + x2 = 0 + -11.2 Reorder the terms: 11.2 + -11.2 + -8x + x2 = 0 + -11.2 Combine like terms: 11.2 + -11.2 = 0.0 0.0 + -8x + x2 = 0 + -11.2 -8x + x2 = 0 + -11.2 Combine like terms: 0 + -11.2 = -11.2 -8x + x2 = -11.2 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 = -11.2 + 16 Reorder the terms: 16 + -8x + x2 = -11.2 + 16 Combine like terms: -11.2 + 16 = 4.8 16 + -8x + x2 = 4.8 Factor a perfect square on the left side: (x + -4)(x + -4) = 4.8 Calculate the square root of the right side: 2.19089023 Break this problem into two subproblems by setting (x + -4) equal to 2.19089023 and -2.19089023.Subproblem 1
x + -4 = 2.19089023 Simplifying x + -4 = 2.19089023 Reorder the terms: -4 + x = 2.19089023 Solving -4 + x = 2.19089023 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 = 2.19089023 + 4 Combine like terms: -4 + 4 = 0 0 + x = 2.19089023 + 4 x = 2.19089023 + 4 Combine like terms: 2.19089023 + 4 = 6.19089023 x = 6.19089023 Simplifying x = 6.19089023Subproblem 2
x + -4 = -2.19089023 Simplifying x + -4 = -2.19089023 Reorder the terms: -4 + x = -2.19089023 Solving -4 + x = -2.19089023 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 = -2.19089023 + 4 Combine like terms: -4 + 4 = 0 0 + x = -2.19089023 + 4 x = -2.19089023 + 4 Combine like terms: -2.19089023 + 4 = 1.80910977 x = 1.80910977 Simplifying x = 1.80910977Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.19089023, 1.80910977}
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