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Simplifying x2 + -12x + -1020 = 0 Reorder the terms: -1020 + -12x + x2 = 0 Solving -1020 + -12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1020' to each side of the equation. -1020 + -12x + 1020 + x2 = 0 + 1020 Reorder the terms: -1020 + 1020 + -12x + x2 = 0 + 1020 Combine like terms: -1020 + 1020 = 0 0 + -12x + x2 = 0 + 1020 -12x + x2 = 0 + 1020 Combine like terms: 0 + 1020 = 1020 -12x + x2 = 1020 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 1020 + 36 Reorder the terms: 36 + -12x + x2 = 1020 + 36 Combine like terms: 1020 + 36 = 1056 36 + -12x + x2 = 1056 Factor a perfect square on the left side: (x + -6)(x + -6) = 1056 Calculate the square root of the right side: 32.496153619 Break this problem into two subproblems by setting (x + -6) equal to 32.496153619 and -32.496153619.Subproblem 1
x + -6 = 32.496153619 Simplifying x + -6 = 32.496153619 Reorder the terms: -6 + x = 32.496153619 Solving -6 + x = 32.496153619 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 32.496153619 + 6 Combine like terms: -6 + 6 = 0 0 + x = 32.496153619 + 6 x = 32.496153619 + 6 Combine like terms: 32.496153619 + 6 = 38.496153619 x = 38.496153619 Simplifying x = 38.496153619Subproblem 2
x + -6 = -32.496153619 Simplifying x + -6 = -32.496153619 Reorder the terms: -6 + x = -32.496153619 Solving -6 + x = -32.496153619 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -32.496153619 + 6 Combine like terms: -6 + 6 = 0 0 + x = -32.496153619 + 6 x = -32.496153619 + 6 Combine like terms: -32.496153619 + 6 = -26.496153619 x = -26.496153619 Simplifying x = -26.496153619Solution
The solution to the problem is based on the solutions from the subproblems. x = {38.496153619, -26.496153619}
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