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Simplifying 21 = -1x2 + 56x + 70 Reorder the terms: 21 = 70 + 56x + -1x2 Solving 21 = 70 + 56x + -1x2 Solving for variable 'x'. Combine like terms: 21 + -70 = -49 -49 + -56x + x2 = 70 + 56x + -1x2 + -70 + -56x + x2 Reorder the terms: -49 + -56x + x2 = 70 + -70 + 56x + -56x + -1x2 + x2 Combine like terms: 70 + -70 = 0 -49 + -56x + x2 = 0 + 56x + -56x + -1x2 + x2 -49 + -56x + x2 = 56x + -56x + -1x2 + x2 Combine like terms: 56x + -56x = 0 -49 + -56x + x2 = 0 + -1x2 + x2 -49 + -56x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -49 + -56x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + -56x + 49 + x2 = 0 + 49 Reorder the terms: -49 + 49 + -56x + x2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + -56x + x2 = 0 + 49 -56x + x2 = 0 + 49 Combine like terms: 0 + 49 = 49 -56x + x2 = 49 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 = 49 + 784 Reorder the terms: 784 + -56x + x2 = 49 + 784 Combine like terms: 49 + 784 = 833 784 + -56x + x2 = 833 Factor a perfect square on the left side: (x + -28)(x + -28) = 833 Calculate the square root of the right side: 28.861739379 Break this problem into two subproblems by setting (x + -28) equal to 28.861739379 and -28.861739379.Subproblem 1
x + -28 = 28.861739379 Simplifying x + -28 = 28.861739379 Reorder the terms: -28 + x = 28.861739379 Solving -28 + x = 28.861739379 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 = 28.861739379 + 28 Combine like terms: -28 + 28 = 0 0 + x = 28.861739379 + 28 x = 28.861739379 + 28 Combine like terms: 28.861739379 + 28 = 56.861739379 x = 56.861739379 Simplifying x = 56.861739379Subproblem 2
x + -28 = -28.861739379 Simplifying x + -28 = -28.861739379 Reorder the terms: -28 + x = -28.861739379 Solving -28 + x = -28.861739379 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 = -28.861739379 + 28 Combine like terms: -28 + 28 = 0 0 + x = -28.861739379 + 28 x = -28.861739379 + 28 Combine like terms: -28.861739379 + 28 = -0.861739379 x = -0.861739379 Simplifying x = -0.861739379Solution
The solution to the problem is based on the solutions from the subproblems. x = {56.861739379, -0.861739379}
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