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Simplifying (5x + -9)(x) = 90 Reorder the terms: (-9 + 5x)(x) = 90 Reorder the terms for easier multiplication: x(-9 + 5x) = 90 (-9 * x + 5x * x) = 90 (-9x + 5x2) = 90 Solving -9x + 5x2 = 90 Solving for variable 'x'. Reorder the terms: -90 + -9x + 5x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -90 + -9x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -18 + -1.8x + x2 = 0 Move the constant term to the right: Add '18' to each side of the equation. -18 + -1.8x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + -1.8x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -1.8x + x2 = 0 + 18 -1.8x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 -1.8x + x2 = 18 The x term is -1.8x. Take half its coefficient (-0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. -1.8x + 0.81 + x2 = 18 + 0.81 Reorder the terms: 0.81 + -1.8x + x2 = 18 + 0.81 Combine like terms: 18 + 0.81 = 18.81 0.81 + -1.8x + x2 = 18.81 Factor a perfect square on the left side: (x + -0.9)(x + -0.9) = 18.81 Calculate the square root of the right side: 4.337049688 Break this problem into two subproblems by setting (x + -0.9) equal to 4.337049688 and -4.337049688.Subproblem 1
x + -0.9 = 4.337049688 Simplifying x + -0.9 = 4.337049688 Reorder the terms: -0.9 + x = 4.337049688 Solving -0.9 + x = 4.337049688 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + x = 4.337049688 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = 4.337049688 + 0.9 x = 4.337049688 + 0.9 Combine like terms: 4.337049688 + 0.9 = 5.237049688 x = 5.237049688 Simplifying x = 5.237049688Subproblem 2
x + -0.9 = -4.337049688 Simplifying x + -0.9 = -4.337049688 Reorder the terms: -0.9 + x = -4.337049688 Solving -0.9 + x = -4.337049688 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + x = -4.337049688 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = -4.337049688 + 0.9 x = -4.337049688 + 0.9 Combine like terms: -4.337049688 + 0.9 = -3.437049688 x = -3.437049688 Simplifying x = -3.437049688Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.237049688, -3.437049688}
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