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Simplifying 2x2 + 8x + -1500 = 0 Reorder the terms: -1500 + 8x + 2x2 = 0 Solving -1500 + 8x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-750 + 4x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-750 + 4x + x2)' equal to zero and attempt to solve: Simplifying -750 + 4x + x2 = 0 Solving -750 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '750' to each side of the equation. -750 + 4x + 750 + x2 = 0 + 750 Reorder the terms: -750 + 750 + 4x + x2 = 0 + 750 Combine like terms: -750 + 750 = 0 0 + 4x + x2 = 0 + 750 4x + x2 = 0 + 750 Combine like terms: 0 + 750 = 750 4x + x2 = 750 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 750 + 4 Reorder the terms: 4 + 4x + x2 = 750 + 4 Combine like terms: 750 + 4 = 754 4 + 4x + x2 = 754 Factor a perfect square on the left side: (x + 2)(x + 2) = 754 Calculate the square root of the right side: 27.459060435 Break this problem into two subproblems by setting (x + 2) equal to 27.459060435 and -27.459060435.Subproblem 1
x + 2 = 27.459060435 Simplifying x + 2 = 27.459060435 Reorder the terms: 2 + x = 27.459060435 Solving 2 + x = 27.459060435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 27.459060435 + -2 Combine like terms: 2 + -2 = 0 0 + x = 27.459060435 + -2 x = 27.459060435 + -2 Combine like terms: 27.459060435 + -2 = 25.459060435 x = 25.459060435 Simplifying x = 25.459060435Subproblem 2
x + 2 = -27.459060435 Simplifying x + 2 = -27.459060435 Reorder the terms: 2 + x = -27.459060435 Solving 2 + x = -27.459060435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -27.459060435 + -2 Combine like terms: 2 + -2 = 0 0 + x = -27.459060435 + -2 x = -27.459060435 + -2 Combine like terms: -27.459060435 + -2 = -29.459060435 x = -29.459060435 Simplifying x = -29.459060435Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.459060435, -29.459060435}Solution
x = {25.459060435, -29.459060435}
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