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Simplifying 3x(4x + -5) = 10x2 + 75 Reorder the terms: 3x(-5 + 4x) = 10x2 + 75 (-5 * 3x + 4x * 3x) = 10x2 + 75 (-15x + 12x2) = 10x2 + 75 Reorder the terms: -15x + 12x2 = 75 + 10x2 Solving -15x + 12x2 = 75 + 10x2 Solving for variable 'x'. Reorder the terms: -75 + -15x + 12x2 + -10x2 = 75 + 10x2 + -75 + -10x2 Combine like terms: 12x2 + -10x2 = 2x2 -75 + -15x + 2x2 = 75 + 10x2 + -75 + -10x2 Reorder the terms: -75 + -15x + 2x2 = 75 + -75 + 10x2 + -10x2 Combine like terms: 75 + -75 = 0 -75 + -15x + 2x2 = 0 + 10x2 + -10x2 -75 + -15x + 2x2 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 -75 + -15x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -37.5 + -7.5x + x2 = 0 Move the constant term to the right: Add '37.5' to each side of the equation. -37.5 + -7.5x + 37.5 + x2 = 0 + 37.5 Reorder the terms: -37.5 + 37.5 + -7.5x + x2 = 0 + 37.5 Combine like terms: -37.5 + 37.5 = 0.0 0.0 + -7.5x + x2 = 0 + 37.5 -7.5x + x2 = 0 + 37.5 Combine like terms: 0 + 37.5 = 37.5 -7.5x + x2 = 37.5 The x term is -7.5x. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5x + 14.0625 + x2 = 37.5 + 14.0625 Reorder the terms: 14.0625 + -7.5x + x2 = 37.5 + 14.0625 Combine like terms: 37.5 + 14.0625 = 51.5625 14.0625 + -7.5x + x2 = 51.5625 Factor a perfect square on the left side: (x + -3.75)(x + -3.75) = 51.5625 Calculate the square root of the right side: 7.180703308 Break this problem into two subproblems by setting (x + -3.75) equal to 7.180703308 and -7.180703308.Subproblem 1
x + -3.75 = 7.180703308 Simplifying x + -3.75 = 7.180703308 Reorder the terms: -3.75 + x = 7.180703308 Solving -3.75 + x = 7.180703308 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = 7.180703308 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = 7.180703308 + 3.75 x = 7.180703308 + 3.75 Combine like terms: 7.180703308 + 3.75 = 10.930703308 x = 10.930703308 Simplifying x = 10.930703308Subproblem 2
x + -3.75 = -7.180703308 Simplifying x + -3.75 = -7.180703308 Reorder the terms: -3.75 + x = -7.180703308 Solving -3.75 + x = -7.180703308 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = -7.180703308 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = -7.180703308 + 3.75 x = -7.180703308 + 3.75 Combine like terms: -7.180703308 + 3.75 = -3.430703308 x = -3.430703308 Simplifying x = -3.430703308Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.930703308, -3.430703308}
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