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Simplifying 0 = 9x2 + 5x + -53 Reorder the terms: 0 = -53 + 5x + 9x2 Solving 0 = -53 + 5x + 9x2 Solving for variable 'x'. Combine like terms: 0 + 53 = 53 53 + -5x + -9x2 = -53 + 5x + 9x2 + 53 + -5x + -9x2 Reorder the terms: 53 + -5x + -9x2 = -53 + 53 + 5x + -5x + 9x2 + -9x2 Combine like terms: -53 + 53 = 0 53 + -5x + -9x2 = 0 + 5x + -5x + 9x2 + -9x2 53 + -5x + -9x2 = 5x + -5x + 9x2 + -9x2 Combine like terms: 5x + -5x = 0 53 + -5x + -9x2 = 0 + 9x2 + -9x2 53 + -5x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 53 + -5x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -5.888888889 + 0.5555555556x + x2 = 0 Move the constant term to the right: Add '5.888888889' to each side of the equation. -5.888888889 + 0.5555555556x + 5.888888889 + x2 = 0 + 5.888888889 Reorder the terms: -5.888888889 + 5.888888889 + 0.5555555556x + x2 = 0 + 5.888888889 Combine like terms: -5.888888889 + 5.888888889 = 0.000000000 0.000000000 + 0.5555555556x + x2 = 0 + 5.888888889 0.5555555556x + x2 = 0 + 5.888888889 Combine like terms: 0 + 5.888888889 = 5.888888889 0.5555555556x + x2 = 5.888888889 The x term is 0.5555555556x. Take half its coefficient (0.2777777778). Square it (0.07716049384) and add it to both sides. Add '0.07716049384' to each side of the equation. 0.5555555556x + 0.07716049384 + x2 = 5.888888889 + 0.07716049384 Reorder the terms: 0.07716049384 + 0.5555555556x + x2 = 5.888888889 + 0.07716049384 Combine like terms: 5.888888889 + 0.07716049384 = 5.96604938284 0.07716049384 + 0.5555555556x + x2 = 5.96604938284 Factor a perfect square on the left side: (x + 0.2777777778)(x + 0.2777777778) = 5.96604938284 Calculate the square root of the right side: 2.442549771 Break this problem into two subproblems by setting (x + 0.2777777778) equal to 2.442549771 and -2.442549771.Subproblem 1
x + 0.2777777778 = 2.442549771 Simplifying x + 0.2777777778 = 2.442549771 Reorder the terms: 0.2777777778 + x = 2.442549771 Solving 0.2777777778 + x = 2.442549771 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2777777778' to each side of the equation. 0.2777777778 + -0.2777777778 + x = 2.442549771 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + x = 2.442549771 + -0.2777777778 x = 2.442549771 + -0.2777777778 Combine like terms: 2.442549771 + -0.2777777778 = 2.1647719932 x = 2.1647719932 Simplifying x = 2.1647719932Subproblem 2
x + 0.2777777778 = -2.442549771 Simplifying x + 0.2777777778 = -2.442549771 Reorder the terms: 0.2777777778 + x = -2.442549771 Solving 0.2777777778 + x = -2.442549771 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2777777778' to each side of the equation. 0.2777777778 + -0.2777777778 + x = -2.442549771 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + x = -2.442549771 + -0.2777777778 x = -2.442549771 + -0.2777777778 Combine like terms: -2.442549771 + -0.2777777778 = -2.7203275488 x = -2.7203275488 Simplifying x = -2.7203275488Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.1647719932, -2.7203275488}
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