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Simplifying x(5x + -7) = 112 Reorder the terms: x(-7 + 5x) = 112 (-7 * x + 5x * x) = 112 (-7x + 5x2) = 112 Solving -7x + 5x2 = 112 Solving for variable 'x'. Reorder the terms: -112 + -7x + 5x2 = 112 + -112 Combine like terms: 112 + -112 = 0 -112 + -7x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -22.4 + -1.4x + x2 = 0 Move the constant term to the right: Add '22.4' to each side of the equation. -22.4 + -1.4x + 22.4 + x2 = 0 + 22.4 Reorder the terms: -22.4 + 22.4 + -1.4x + x2 = 0 + 22.4 Combine like terms: -22.4 + 22.4 = 0.0 0.0 + -1.4x + x2 = 0 + 22.4 -1.4x + x2 = 0 + 22.4 Combine like terms: 0 + 22.4 = 22.4 -1.4x + x2 = 22.4 The x term is -1.4x. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4x + 0.49 + x2 = 22.4 + 0.49 Reorder the terms: 0.49 + -1.4x + x2 = 22.4 + 0.49 Combine like terms: 22.4 + 0.49 = 22.89 0.49 + -1.4x + x2 = 22.89 Factor a perfect square on the left side: (x + -0.7)(x + -0.7) = 22.89 Calculate the square root of the right side: 4.784349486 Break this problem into two subproblems by setting (x + -0.7) equal to 4.784349486 and -4.784349486.Subproblem 1
x + -0.7 = 4.784349486 Simplifying x + -0.7 = 4.784349486 Reorder the terms: -0.7 + x = 4.784349486 Solving -0.7 + x = 4.784349486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = 4.784349486 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = 4.784349486 + 0.7 x = 4.784349486 + 0.7 Combine like terms: 4.784349486 + 0.7 = 5.484349486 x = 5.484349486 Simplifying x = 5.484349486Subproblem 2
x + -0.7 = -4.784349486 Simplifying x + -0.7 = -4.784349486 Reorder the terms: -0.7 + x = -4.784349486 Solving -0.7 + x = -4.784349486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = -4.784349486 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = -4.784349486 + 0.7 x = -4.784349486 + 0.7 Combine like terms: -4.784349486 + 0.7 = -4.084349486 x = -4.084349486 Simplifying x = -4.084349486Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.484349486, -4.084349486}
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