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Simplifying -5x(x + 4) + -3(x + -1) = -7x + -31 Reorder the terms: -5x(4 + x) + -3(x + -1) = -7x + -31 (4 * -5x + x * -5x) + -3(x + -1) = -7x + -31 (-20x + -5x2) + -3(x + -1) = -7x + -31 Reorder the terms: -20x + -5x2 + -3(-1 + x) = -7x + -31 -20x + -5x2 + (-1 * -3 + x * -3) = -7x + -31 -20x + -5x2 + (3 + -3x) = -7x + -31 Reorder the terms: 3 + -20x + -3x + -5x2 = -7x + -31 Combine like terms: -20x + -3x = -23x 3 + -23x + -5x2 = -7x + -31 Reorder the terms: 3 + -23x + -5x2 = -31 + -7x Solving 3 + -23x + -5x2 = -31 + -7x Solving for variable 'x'. Reorder the terms: 3 + 31 + -23x + 7x + -5x2 = -31 + -7x + 31 + 7x Combine like terms: 3 + 31 = 34 34 + -23x + 7x + -5x2 = -31 + -7x + 31 + 7x Combine like terms: -23x + 7x = -16x 34 + -16x + -5x2 = -31 + -7x + 31 + 7x Reorder the terms: 34 + -16x + -5x2 = -31 + 31 + -7x + 7x Combine like terms: -31 + 31 = 0 34 + -16x + -5x2 = 0 + -7x + 7x 34 + -16x + -5x2 = -7x + 7x Combine like terms: -7x + 7x = 0 34 + -16x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -6.8 + 3.2x + x2 = 0 Move the constant term to the right: Add '6.8' to each side of the equation. -6.8 + 3.2x + 6.8 + x2 = 0 + 6.8 Reorder the terms: -6.8 + 6.8 + 3.2x + x2 = 0 + 6.8 Combine like terms: -6.8 + 6.8 = 0.0 0.0 + 3.2x + x2 = 0 + 6.8 3.2x + x2 = 0 + 6.8 Combine like terms: 0 + 6.8 = 6.8 3.2x + x2 = 6.8 The x term is 3.2x. Take half its coefficient (1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. 3.2x + 2.56 + x2 = 6.8 + 2.56 Reorder the terms: 2.56 + 3.2x + x2 = 6.8 + 2.56 Combine like terms: 6.8 + 2.56 = 9.36 2.56 + 3.2x + x2 = 9.36 Factor a perfect square on the left side: (x + 1.6)(x + 1.6) = 9.36 Calculate the square root of the right side: 3.059411708 Break this problem into two subproblems by setting (x + 1.6) equal to 3.059411708 and -3.059411708.Subproblem 1
x + 1.6 = 3.059411708 Simplifying x + 1.6 = 3.059411708 Reorder the terms: 1.6 + x = 3.059411708 Solving 1.6 + x = 3.059411708 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + x = 3.059411708 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + x = 3.059411708 + -1.6 x = 3.059411708 + -1.6 Combine like terms: 3.059411708 + -1.6 = 1.459411708 x = 1.459411708 Simplifying x = 1.459411708Subproblem 2
x + 1.6 = -3.059411708 Simplifying x + 1.6 = -3.059411708 Reorder the terms: 1.6 + x = -3.059411708 Solving 1.6 + x = -3.059411708 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + x = -3.059411708 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + x = -3.059411708 + -1.6 x = -3.059411708 + -1.6 Combine like terms: -3.059411708 + -1.6 = -4.659411708 x = -4.659411708 Simplifying x = -4.659411708Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.459411708, -4.659411708}
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