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Simplifying (3x + -10)(x + -20) + -1(2x + 5)(2x + 5) = 0 Reorder the terms: (-10 + 3x)(x + -20) + -1(2x + 5)(2x + 5) = 0 Reorder the terms: (-10 + 3x)(-20 + x) + -1(2x + 5)(2x + 5) = 0 Multiply (-10 + 3x) * (-20 + x) (-10(-20 + x) + 3x * (-20 + x)) + -1(2x + 5)(2x + 5) = 0 ((-20 * -10 + x * -10) + 3x * (-20 + x)) + -1(2x + 5)(2x + 5) = 0 ((200 + -10x) + 3x * (-20 + x)) + -1(2x + 5)(2x + 5) = 0 (200 + -10x + (-20 * 3x + x * 3x)) + -1(2x + 5)(2x + 5) = 0 (200 + -10x + (-60x + 3x2)) + -1(2x + 5)(2x + 5) = 0 Combine like terms: -10x + -60x = -70x (200 + -70x + 3x2) + -1(2x + 5)(2x + 5) = 0 Reorder the terms: 200 + -70x + 3x2 + -1(5 + 2x)(2x + 5) = 0 Reorder the terms: 200 + -70x + 3x2 + -1(5 + 2x)(5 + 2x) = 0 Multiply (5 + 2x) * (5 + 2x) 200 + -70x + 3x2 + -1(5(5 + 2x) + 2x * (5 + 2x)) = 0 200 + -70x + 3x2 + -1((5 * 5 + 2x * 5) + 2x * (5 + 2x)) = 0 200 + -70x + 3x2 + -1((25 + 10x) + 2x * (5 + 2x)) = 0 200 + -70x + 3x2 + -1(25 + 10x + (5 * 2x + 2x * 2x)) = 0 200 + -70x + 3x2 + -1(25 + 10x + (10x + 4x2)) = 0 Combine like terms: 10x + 10x = 20x 200 + -70x + 3x2 + -1(25 + 20x + 4x2) = 0 200 + -70x + 3x2 + (25 * -1 + 20x * -1 + 4x2 * -1) = 0 200 + -70x + 3x2 + (-25 + -20x + -4x2) = 0 Reorder the terms: 200 + -25 + -70x + -20x + 3x2 + -4x2 = 0 Combine like terms: 200 + -25 = 175 175 + -70x + -20x + 3x2 + -4x2 = 0 Combine like terms: -70x + -20x = -90x 175 + -90x + 3x2 + -4x2 = 0 Combine like terms: 3x2 + -4x2 = -1x2 175 + -90x + -1x2 = 0 Solving 175 + -90x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -175 + 90x + x2 = 0 Move the constant term to the right: Add '175' to each side of the equation. -175 + 90x + 175 + x2 = 0 + 175 Reorder the terms: -175 + 175 + 90x + x2 = 0 + 175 Combine like terms: -175 + 175 = 0 0 + 90x + x2 = 0 + 175 90x + x2 = 0 + 175 Combine like terms: 0 + 175 = 175 90x + x2 = 175 The x term is 90x. Take half its coefficient (45). Square it (2025) and add it to both sides. Add '2025' to each side of the equation. 90x + 2025 + x2 = 175 + 2025 Reorder the terms: 2025 + 90x + x2 = 175 + 2025 Combine like terms: 175 + 2025 = 2200 2025 + 90x + x2 = 2200 Factor a perfect square on the left side: (x + 45)(x + 45) = 2200 Calculate the square root of the right side: 46.904157598 Break this problem into two subproblems by setting (x + 45) equal to 46.904157598 and -46.904157598.Subproblem 1
x + 45 = 46.904157598 Simplifying x + 45 = 46.904157598 Reorder the terms: 45 + x = 46.904157598 Solving 45 + x = 46.904157598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-45' to each side of the equation. 45 + -45 + x = 46.904157598 + -45 Combine like terms: 45 + -45 = 0 0 + x = 46.904157598 + -45 x = 46.904157598 + -45 Combine like terms: 46.904157598 + -45 = 1.904157598 x = 1.904157598 Simplifying x = 1.904157598Subproblem 2
x + 45 = -46.904157598 Simplifying x + 45 = -46.904157598 Reorder the terms: 45 + x = -46.904157598 Solving 45 + x = -46.904157598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-45' to each side of the equation. 45 + -45 + x = -46.904157598 + -45 Combine like terms: 45 + -45 = 0 0 + x = -46.904157598 + -45 x = -46.904157598 + -45 Combine like terms: -46.904157598 + -45 = -91.904157598 x = -91.904157598 Simplifying x = -91.904157598Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.904157598, -91.904157598}
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