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Simplifying 29 = -1x2 + 56x + 70 Reorder the terms: 29 = 70 + 56x + -1x2 Solving 29 = 70 + 56x + -1x2 Solving for variable 'x'. Combine like terms: 29 + -70 = -41 -41 + -56x + x2 = 70 + 56x + -1x2 + -70 + -56x + x2 Reorder the terms: -41 + -56x + x2 = 70 + -70 + 56x + -56x + -1x2 + x2 Combine like terms: 70 + -70 = 0 -41 + -56x + x2 = 0 + 56x + -56x + -1x2 + x2 -41 + -56x + x2 = 56x + -56x + -1x2 + x2 Combine like terms: 56x + -56x = 0 -41 + -56x + x2 = 0 + -1x2 + x2 -41 + -56x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -41 + -56x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '41' to each side of the equation. -41 + -56x + 41 + x2 = 0 + 41 Reorder the terms: -41 + 41 + -56x + x2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + -56x + x2 = 0 + 41 -56x + x2 = 0 + 41 Combine like terms: 0 + 41 = 41 -56x + x2 = 41 The x term is -56x. Take half its coefficient (-28). Square it (784) and add it to both sides. Add '784' to each side of the equation. -56x + 784 + x2 = 41 + 784 Reorder the terms: 784 + -56x + x2 = 41 + 784 Combine like terms: 41 + 784 = 825 784 + -56x + x2 = 825 Factor a perfect square on the left side: (x + -28)(x + -28) = 825 Calculate the square root of the right side: 28.722813233 Break this problem into two subproblems by setting (x + -28) equal to 28.722813233 and -28.722813233.Subproblem 1
x + -28 = 28.722813233 Simplifying x + -28 = 28.722813233 Reorder the terms: -28 + x = 28.722813233 Solving -28 + x = 28.722813233 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '28' to each side of the equation. -28 + 28 + x = 28.722813233 + 28 Combine like terms: -28 + 28 = 0 0 + x = 28.722813233 + 28 x = 28.722813233 + 28 Combine like terms: 28.722813233 + 28 = 56.722813233 x = 56.722813233 Simplifying x = 56.722813233Subproblem 2
x + -28 = -28.722813233 Simplifying x + -28 = -28.722813233 Reorder the terms: -28 + x = -28.722813233 Solving -28 + x = -28.722813233 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '28' to each side of the equation. -28 + 28 + x = -28.722813233 + 28 Combine like terms: -28 + 28 = 0 0 + x = -28.722813233 + 28 x = -28.722813233 + 28 Combine like terms: -28.722813233 + 28 = -0.722813233 x = -0.722813233 Simplifying x = -0.722813233Solution
The solution to the problem is based on the solutions from the subproblems. x = {56.722813233, -0.722813233}
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