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Simplifying 36x2 + -65x + -1 = 0 Reorder the terms: -1 + -65x + 36x2 = 0 Solving -1 + -65x + 36x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -0.02777777778 + -1.805555556x + x2 = 0 Move the constant term to the right: Add '0.02777777778' to each side of the equation. -0.02777777778 + -1.805555556x + 0.02777777778 + x2 = 0 + 0.02777777778 Reorder the terms: -0.02777777778 + 0.02777777778 + -1.805555556x + x2 = 0 + 0.02777777778 Combine like terms: -0.02777777778 + 0.02777777778 = 0.00000000000 0.00000000000 + -1.805555556x + x2 = 0 + 0.02777777778 -1.805555556x + x2 = 0 + 0.02777777778 Combine like terms: 0 + 0.02777777778 = 0.02777777778 -1.805555556x + x2 = 0.02777777778 The x term is -1.805555556x. Take half its coefficient (-0.902777778). Square it (0.8150077165) and add it to both sides. Add '0.8150077165' to each side of the equation. -1.805555556x + 0.8150077165 + x2 = 0.02777777778 + 0.8150077165 Reorder the terms: 0.8150077165 + -1.805555556x + x2 = 0.02777777778 + 0.8150077165 Combine like terms: 0.02777777778 + 0.8150077165 = 0.84278549428 0.8150077165 + -1.805555556x + x2 = 0.84278549428 Factor a perfect square on the left side: (x + -0.902777778)(x + -0.902777778) = 0.84278549428 Calculate the square root of the right side: 0.918033493 Break this problem into two subproblems by setting (x + -0.902777778) equal to 0.918033493 and -0.918033493.Subproblem 1
x + -0.902777778 = 0.918033493 Simplifying x + -0.902777778 = 0.918033493 Reorder the terms: -0.902777778 + x = 0.918033493 Solving -0.902777778 + x = 0.918033493 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.902777778' to each side of the equation. -0.902777778 + 0.902777778 + x = 0.918033493 + 0.902777778 Combine like terms: -0.902777778 + 0.902777778 = 0.000000000 0.000000000 + x = 0.918033493 + 0.902777778 x = 0.918033493 + 0.902777778 Combine like terms: 0.918033493 + 0.902777778 = 1.820811271 x = 1.820811271 Simplifying x = 1.820811271Subproblem 2
x + -0.902777778 = -0.918033493 Simplifying x + -0.902777778 = -0.918033493 Reorder the terms: -0.902777778 + x = -0.918033493 Solving -0.902777778 + x = -0.918033493 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.902777778' to each side of the equation. -0.902777778 + 0.902777778 + x = -0.918033493 + 0.902777778 Combine like terms: -0.902777778 + 0.902777778 = 0.000000000 0.000000000 + x = -0.918033493 + 0.902777778 x = -0.918033493 + 0.902777778 Combine like terms: -0.918033493 + 0.902777778 = -0.015255715 x = -0.015255715 Simplifying x = -0.015255715Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.820811271, -0.015255715}
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