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Simplifying (2x + 1)(x + -10) = 90 Reorder the terms: (1 + 2x)(x + -10) = 90 Reorder the terms: (1 + 2x)(-10 + x) = 90 Multiply (1 + 2x) * (-10 + x) (1(-10 + x) + 2x * (-10 + x)) = 90 ((-10 * 1 + x * 1) + 2x * (-10 + x)) = 90 ((-10 + 1x) + 2x * (-10 + x)) = 90 (-10 + 1x + (-10 * 2x + x * 2x)) = 90 (-10 + 1x + (-20x + 2x2)) = 90 Combine like terms: 1x + -20x = -19x (-10 + -19x + 2x2) = 90 Solving -10 + -19x + 2x2 = 90 Solving for variable 'x'. Reorder the terms: -10 + -90 + -19x + 2x2 = 90 + -90 Combine like terms: -10 + -90 = -100 -100 + -19x + 2x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -100 + -19x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -50 + -9.5x + x2 = 0 Move the constant term to the right: Add '50' to each side of the equation. -50 + -9.5x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + -9.5x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + -9.5x + x2 = 0 + 50 -9.5x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 -9.5x + x2 = 50 The x term is -9.5x. Take half its coefficient (-4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. -9.5x + 22.5625 + x2 = 50 + 22.5625 Reorder the terms: 22.5625 + -9.5x + x2 = 50 + 22.5625 Combine like terms: 50 + 22.5625 = 72.5625 22.5625 + -9.5x + x2 = 72.5625 Factor a perfect square on the left side: (x + -4.75)(x + -4.75) = 72.5625 Calculate the square root of the right side: 8.518362519 Break this problem into two subproblems by setting (x + -4.75) equal to 8.518362519 and -8.518362519.Subproblem 1
x + -4.75 = 8.518362519 Simplifying x + -4.75 = 8.518362519 Reorder the terms: -4.75 + x = 8.518362519 Solving -4.75 + x = 8.518362519 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = 8.518362519 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = 8.518362519 + 4.75 x = 8.518362519 + 4.75 Combine like terms: 8.518362519 + 4.75 = 13.268362519 x = 13.268362519 Simplifying x = 13.268362519Subproblem 2
x + -4.75 = -8.518362519 Simplifying x + -4.75 = -8.518362519 Reorder the terms: -4.75 + x = -8.518362519 Solving -4.75 + x = -8.518362519 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = -8.518362519 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = -8.518362519 + 4.75 x = -8.518362519 + 4.75 Combine like terms: -8.518362519 + 4.75 = -3.768362519 x = -3.768362519 Simplifying x = -3.768362519Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.268362519, -3.768362519}
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