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Simplifying 1008 = 2x2 + 8x + -1072 Reorder the terms: 1008 = -1072 + 8x + 2x2 Solving 1008 = -1072 + 8x + 2x2 Solving for variable 'x'. Combine like terms: 1008 + 1072 = 2080 2080 + -8x + -2x2 = -1072 + 8x + 2x2 + 1072 + -8x + -2x2 Reorder the terms: 2080 + -8x + -2x2 = -1072 + 1072 + 8x + -8x + 2x2 + -2x2 Combine like terms: -1072 + 1072 = 0 2080 + -8x + -2x2 = 0 + 8x + -8x + 2x2 + -2x2 2080 + -8x + -2x2 = 8x + -8x + 2x2 + -2x2 Combine like terms: 8x + -8x = 0 2080 + -8x + -2x2 = 0 + 2x2 + -2x2 2080 + -8x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 2080 + -8x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(1040 + -4x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1040 + -4x + -1x2)' equal to zero and attempt to solve: Simplifying 1040 + -4x + -1x2 = 0 Solving 1040 + -4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1040 + 4x + x2 = 0 Move the constant term to the right: Add '1040' to each side of the equation. -1040 + 4x + 1040 + x2 = 0 + 1040 Reorder the terms: -1040 + 1040 + 4x + x2 = 0 + 1040 Combine like terms: -1040 + 1040 = 0 0 + 4x + x2 = 0 + 1040 4x + x2 = 0 + 1040 Combine like terms: 0 + 1040 = 1040 4x + x2 = 1040 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 = 1040 + 4 Reorder the terms: 4 + 4x + x2 = 1040 + 4 Combine like terms: 1040 + 4 = 1044 4 + 4x + x2 = 1044 Factor a perfect square on the left side: (x + 2)(x + 2) = 1044 Calculate the square root of the right side: 32.310988843 Break this problem into two subproblems by setting (x + 2) equal to 32.310988843 and -32.310988843.Subproblem 1
x + 2 = 32.310988843 Simplifying x + 2 = 32.310988843 Reorder the terms: 2 + x = 32.310988843 Solving 2 + x = 32.310988843 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 = 32.310988843 + -2 Combine like terms: 2 + -2 = 0 0 + x = 32.310988843 + -2 x = 32.310988843 + -2 Combine like terms: 32.310988843 + -2 = 30.310988843 x = 30.310988843 Simplifying x = 30.310988843Subproblem 2
x + 2 = -32.310988843 Simplifying x + 2 = -32.310988843 Reorder the terms: 2 + x = -32.310988843 Solving 2 + x = -32.310988843 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 = -32.310988843 + -2 Combine like terms: 2 + -2 = 0 0 + x = -32.310988843 + -2 x = -32.310988843 + -2 Combine like terms: -32.310988843 + -2 = -34.310988843 x = -34.310988843 Simplifying x = -34.310988843Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.310988843, -34.310988843}Solution
x = {30.310988843, -34.310988843}
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