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Simplifying 0 = 1 + 15x + -15x2 Solving 0 = 1 + 15x + -15x2 Solving for variable 'x'. Combine like terms: 0 + -1 = -1 -1 + -15x + 15x2 = 1 + 15x + -15x2 + -1 + -15x + 15x2 Reorder the terms: -1 + -15x + 15x2 = 1 + -1 + 15x + -15x + -15x2 + 15x2 Combine like terms: 1 + -1 = 0 -1 + -15x + 15x2 = 0 + 15x + -15x + -15x2 + 15x2 -1 + -15x + 15x2 = 15x + -15x + -15x2 + 15x2 Combine like terms: 15x + -15x = 0 -1 + -15x + 15x2 = 0 + -15x2 + 15x2 -1 + -15x + 15x2 = -15x2 + 15x2 Combine like terms: -15x2 + 15x2 = 0 -1 + -15x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.06666666667 + -1x + x2 = 0 Move the constant term to the right: Add '0.06666666667' to each side of the equation. -0.06666666667 + -1x + 0.06666666667 + x2 = 0 + 0.06666666667 Reorder the terms: -0.06666666667 + 0.06666666667 + -1x + x2 = 0 + 0.06666666667 Combine like terms: -0.06666666667 + 0.06666666667 = 0.00000000000 0.00000000000 + -1x + x2 = 0 + 0.06666666667 -1x + x2 = 0 + 0.06666666667 Combine like terms: 0 + 0.06666666667 = 0.06666666667 -1x + x2 = 0.06666666667 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 0.06666666667 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 0.06666666667 + 0.25 Combine like terms: 0.06666666667 + 0.25 = 0.31666666667 0.25 + -1x + x2 = 0.31666666667 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.31666666667 Calculate the square root of the right side: 0.562731434 Break this problem into two subproblems by setting (x + -0.5) equal to 0.562731434 and -0.562731434.Subproblem 1
x + -0.5 = 0.562731434 Simplifying x + -0.5 = 0.562731434 Reorder the terms: -0.5 + x = 0.562731434 Solving -0.5 + x = 0.562731434 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.562731434 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.562731434 + 0.5 x = 0.562731434 + 0.5 Combine like terms: 0.562731434 + 0.5 = 1.062731434 x = 1.062731434 Simplifying x = 1.062731434Subproblem 2
x + -0.5 = -0.562731434 Simplifying x + -0.5 = -0.562731434 Reorder the terms: -0.5 + x = -0.562731434 Solving -0.5 + x = -0.562731434 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -0.562731434 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.562731434 + 0.5 x = -0.562731434 + 0.5 Combine like terms: -0.562731434 + 0.5 = -0.062731434 x = -0.062731434 Simplifying x = -0.062731434Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.062731434, -0.062731434}
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