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Simplifying 2x2 + 80x + -1288 = 0 Reorder the terms: -1288 + 80x + 2x2 = 0 Solving -1288 + 80x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-644 + 40x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-644 + 40x + x2)' equal to zero and attempt to solve: Simplifying -644 + 40x + x2 = 0 Solving -644 + 40x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '644' to each side of the equation. -644 + 40x + 644 + x2 = 0 + 644 Reorder the terms: -644 + 644 + 40x + x2 = 0 + 644 Combine like terms: -644 + 644 = 0 0 + 40x + x2 = 0 + 644 40x + x2 = 0 + 644 Combine like terms: 0 + 644 = 644 40x + x2 = 644 The x term is 40x. Take half its coefficient (20). Square it (400) and add it to both sides. Add '400' to each side of the equation. 40x + 400 + x2 = 644 + 400 Reorder the terms: 400 + 40x + x2 = 644 + 400 Combine like terms: 644 + 400 = 1044 400 + 40x + x2 = 1044 Factor a perfect square on the left side: (x + 20)(x + 20) = 1044 Calculate the square root of the right side: 32.310988843 Break this problem into two subproblems by setting (x + 20) equal to 32.310988843 and -32.310988843.Subproblem 1
x + 20 = 32.310988843 Simplifying x + 20 = 32.310988843 Reorder the terms: 20 + x = 32.310988843 Solving 20 + x = 32.310988843 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = 32.310988843 + -20 Combine like terms: 20 + -20 = 0 0 + x = 32.310988843 + -20 x = 32.310988843 + -20 Combine like terms: 32.310988843 + -20 = 12.310988843 x = 12.310988843 Simplifying x = 12.310988843Subproblem 2
x + 20 = -32.310988843 Simplifying x + 20 = -32.310988843 Reorder the terms: 20 + x = -32.310988843 Solving 20 + x = -32.310988843 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = -32.310988843 + -20 Combine like terms: 20 + -20 = 0 0 + x = -32.310988843 + -20 x = -32.310988843 + -20 Combine like terms: -32.310988843 + -20 = -52.310988843 x = -52.310988843 Simplifying x = -52.310988843Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.310988843, -52.310988843}Solution
x = {12.310988843, -52.310988843}
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