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Simplifying 40 = 2(1.25x + -4) * x + x Reorder the terms: 40 = 2(-4 + 1.25x) * x + x Reorder the terms for easier multiplication: 40 = 2x(-4 + 1.25x) + x 40 = (-4 * 2x + 1.25x * 2x) + x 40 = (-8x + 2.5x2) + x Reorder the terms: 40 = -8x + x + 2.5x2 Combine like terms: -8x + x = -7x 40 = -7x + 2.5x2 Solving 40 = -7x + 2.5x2 Solving for variable 'x'. Reorder the terms: 40 + 7x + -2.5x2 = -7x + 7x + 2.5x2 + -2.5x2 Combine like terms: -7x + 7x = 0 40 + 7x + -2.5x2 = 0 + 2.5x2 + -2.5x2 40 + 7x + -2.5x2 = 2.5x2 + -2.5x2 Combine like terms: 2.5x2 + -2.5x2 = 0.0 40 + 7x + -2.5x2 = 0.0 Begin completing the square. Divide all terms by -2.5 the coefficient of the squared term: Divide each side by '-2.5'. -16 + -2.8x + x2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + -2.8x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + -2.8x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -2.8x + x2 = 0 + 16 -2.8x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 -2.8x + x2 = 16 The x term is -2.8x. Take half its coefficient (-1.4). Square it (1.96) and add it to both sides. Add '1.96' to each side of the equation. -2.8x + 1.96 + x2 = 16 + 1.96 Reorder the terms: 1.96 + -2.8x + x2 = 16 + 1.96 Combine like terms: 16 + 1.96 = 17.96 1.96 + -2.8x + x2 = 17.96 Factor a perfect square on the left side: (x + -1.4)(x + -1.4) = 17.96 Calculate the square root of the right side: 4.23792402 Break this problem into two subproblems by setting (x + -1.4) equal to 4.23792402 and -4.23792402.Subproblem 1
x + -1.4 = 4.23792402 Simplifying x + -1.4 = 4.23792402 Reorder the terms: -1.4 + x = 4.23792402 Solving -1.4 + x = 4.23792402 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + x = 4.23792402 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + x = 4.23792402 + 1.4 x = 4.23792402 + 1.4 Combine like terms: 4.23792402 + 1.4 = 5.63792402 x = 5.63792402 Simplifying x = 5.63792402Subproblem 2
x + -1.4 = -4.23792402 Simplifying x + -1.4 = -4.23792402 Reorder the terms: -1.4 + x = -4.23792402 Solving -1.4 + x = -4.23792402 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + x = -4.23792402 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + x = -4.23792402 + 1.4 x = -4.23792402 + 1.4 Combine like terms: -4.23792402 + 1.4 = -2.83792402 x = -2.83792402 Simplifying x = -2.83792402Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.63792402, -2.83792402}
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