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Simplifying -9x2 + -2x + 1 = -557 Reorder the terms: 1 + -2x + -9x2 = -557 Solving 1 + -2x + -9x2 = -557 Solving for variable 'x'. Reorder the terms: 1 + 557 + -2x + -9x2 = -557 + 557 Combine like terms: 1 + 557 = 558 558 + -2x + -9x2 = -557 + 557 Combine like terms: -557 + 557 = 0 558 + -2x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -62 + 0.2222222222x + x2 = 0 Move the constant term to the right: Add '62' to each side of the equation. -62 + 0.2222222222x + 62 + x2 = 0 + 62 Reorder the terms: -62 + 62 + 0.2222222222x + x2 = 0 + 62 Combine like terms: -62 + 62 = 0 0 + 0.2222222222x + x2 = 0 + 62 0.2222222222x + x2 = 0 + 62 Combine like terms: 0 + 62 = 62 0.2222222222x + x2 = 62 The x term is 0.2222222222x. Take half its coefficient (0.1111111111). Square it (0.01234567901) and add it to both sides. Add '0.01234567901' to each side of the equation. 0.2222222222x + 0.01234567901 + x2 = 62 + 0.01234567901 Reorder the terms: 0.01234567901 + 0.2222222222x + x2 = 62 + 0.01234567901 Combine like terms: 62 + 0.01234567901 = 62.01234567901 0.01234567901 + 0.2222222222x + x2 = 62.01234567901 Factor a perfect square on the left side: (x + 0.1111111111)(x + 0.1111111111) = 62.01234567901 Calculate the square root of the right side: 7.874791786 Break this problem into two subproblems by setting (x + 0.1111111111) equal to 7.874791786 and -7.874791786.Subproblem 1
x + 0.1111111111 = 7.874791786 Simplifying x + 0.1111111111 = 7.874791786 Reorder the terms: 0.1111111111 + x = 7.874791786 Solving 0.1111111111 + x = 7.874791786 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1111111111' to each side of the equation. 0.1111111111 + -0.1111111111 + x = 7.874791786 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + x = 7.874791786 + -0.1111111111 x = 7.874791786 + -0.1111111111 Combine like terms: 7.874791786 + -0.1111111111 = 7.7636806749 x = 7.7636806749 Simplifying x = 7.7636806749Subproblem 2
x + 0.1111111111 = -7.874791786 Simplifying x + 0.1111111111 = -7.874791786 Reorder the terms: 0.1111111111 + x = -7.874791786 Solving 0.1111111111 + x = -7.874791786 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1111111111' to each side of the equation. 0.1111111111 + -0.1111111111 + x = -7.874791786 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + x = -7.874791786 + -0.1111111111 x = -7.874791786 + -0.1111111111 Combine like terms: -7.874791786 + -0.1111111111 = -7.9859028971 x = -7.9859028971 Simplifying x = -7.9859028971Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.7636806749, -7.9859028971}
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