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Simplifying 15x2 + 2x + -0.06 = 0 Reorder the terms: -0.06 + 2x + 15x2 = 0 Solving -0.06 + 2x + 15x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.004 + 0.1333333333x + x2 = 0 Move the constant term to the right: Add '0.004' to each side of the equation. -0.004 + 0.1333333333x + 0.004 + x2 = 0 + 0.004 Reorder the terms: -0.004 + 0.004 + 0.1333333333x + x2 = 0 + 0.004 Combine like terms: -0.004 + 0.004 = 0.000 0.000 + 0.1333333333x + x2 = 0 + 0.004 0.1333333333x + x2 = 0 + 0.004 Combine like terms: 0 + 0.004 = 0.004 0.1333333333x + x2 = 0.004 The x term is 0.1333333333x. Take half its coefficient (0.06666666665). Square it (0.004444444442) and add it to both sides. Add '0.004444444442' to each side of the equation. 0.1333333333x + 0.004444444442 + x2 = 0.004 + 0.004444444442 Reorder the terms: 0.004444444442 + 0.1333333333x + x2 = 0.004 + 0.004444444442 Combine like terms: 0.004 + 0.004444444442 = 0.008444444442 0.004444444442 + 0.1333333333x + x2 = 0.008444444442 Factor a perfect square on the left side: (x + 0.06666666665)(x + 0.06666666665) = 0.008444444442 Calculate the square root of the right side: 0.091893658 Break this problem into two subproblems by setting (x + 0.06666666665) equal to 0.091893658 and -0.091893658.Subproblem 1
x + 0.06666666665 = 0.091893658 Simplifying x + 0.06666666665 = 0.091893658 Reorder the terms: 0.06666666665 + x = 0.091893658 Solving 0.06666666665 + x = 0.091893658 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.06666666665' to each side of the equation. 0.06666666665 + -0.06666666665 + x = 0.091893658 + -0.06666666665 Combine like terms: 0.06666666665 + -0.06666666665 = 0.00000000000 0.00000000000 + x = 0.091893658 + -0.06666666665 x = 0.091893658 + -0.06666666665 Combine like terms: 0.091893658 + -0.06666666665 = 0.02522699135 x = 0.02522699135 Simplifying x = 0.02522699135Subproblem 2
x + 0.06666666665 = -0.091893658 Simplifying x + 0.06666666665 = -0.091893658 Reorder the terms: 0.06666666665 + x = -0.091893658 Solving 0.06666666665 + x = -0.091893658 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.06666666665' to each side of the equation. 0.06666666665 + -0.06666666665 + x = -0.091893658 + -0.06666666665 Combine like terms: 0.06666666665 + -0.06666666665 = 0.00000000000 0.00000000000 + x = -0.091893658 + -0.06666666665 x = -0.091893658 + -0.06666666665 Combine like terms: -0.091893658 + -0.06666666665 = -0.15856032465 x = -0.15856032465 Simplifying x = -0.15856032465Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.02522699135, -0.15856032465}
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