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Simplifying 0.00919 = x(1 + -12.353x) 0.00919 = (1 * x + -12.353x * x) 0.00919 = (1x + -12.353x2) Solving 0.00919 = 1x + -12.353x2 Solving for variable 'x'. Reorder the terms: 0.00919 + -1x + 12.353x2 = 1x + -1x + -12.353x2 + 12.353x2 Combine like terms: 1x + -1x = 0 0.00919 + -1x + 12.353x2 = 0 + -12.353x2 + 12.353x2 0.00919 + -1x + 12.353x2 = -12.353x2 + 12.353x2 Combine like terms: -12.353x2 + 12.353x2 = 0.000 0.00919 + -1x + 12.353x2 = 0.000 Begin completing the square. Divide all terms by 12.353 the coefficient of the squared term: Divide each side by '12.353'. 0.0007439488383 + -0.08095199547x + x2 = 0 Move the constant term to the right: Add '-0.0007439488383' to each side of the equation. 0.0007439488383 + -0.08095199547x + -0.0007439488383 + x2 = 0 + -0.0007439488383 Reorder the terms: 0.0007439488383 + -0.0007439488383 + -0.08095199547x + x2 = 0 + -0.0007439488383 Combine like terms: 0.0007439488383 + -0.0007439488383 = 0.0000000000000 0.0000000000000 + -0.08095199547x + x2 = 0 + -0.0007439488383 -0.08095199547x + x2 = 0 + -0.0007439488383 Combine like terms: 0 + -0.0007439488383 = -0.0007439488383 -0.08095199547x + x2 = -0.0007439488383 The x term is -0.08095199547x. Take half its coefficient (-0.04047599774). Square it (0.001638306393) and add it to both sides. Add '0.001638306393' to each side of the equation. -0.08095199547x + 0.001638306393 + x2 = -0.0007439488383 + 0.001638306393 Reorder the terms: 0.001638306393 + -0.08095199547x + x2 = -0.0007439488383 + 0.001638306393 Combine like terms: -0.0007439488383 + 0.001638306393 = 0.0008943575547 0.001638306393 + -0.08095199547x + x2 = 0.0008943575547 Factor a perfect square on the left side: (x + -0.04047599774)(x + -0.04047599774) = 0.0008943575547 Calculate the square root of the right side: 0.029905811 Break this problem into two subproblems by setting (x + -0.04047599774) equal to 0.029905811 and -0.029905811.Subproblem 1
x + -0.04047599774 = 0.029905811 Simplifying x + -0.04047599774 = 0.029905811 Reorder the terms: -0.04047599774 + x = 0.029905811 Solving -0.04047599774 + x = 0.029905811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04047599774' to each side of the equation. -0.04047599774 + 0.04047599774 + x = 0.029905811 + 0.04047599774 Combine like terms: -0.04047599774 + 0.04047599774 = 0.00000000000 0.00000000000 + x = 0.029905811 + 0.04047599774 x = 0.029905811 + 0.04047599774 Combine like terms: 0.029905811 + 0.04047599774 = 0.07038180874 x = 0.07038180874 Simplifying x = 0.07038180874Subproblem 2
x + -0.04047599774 = -0.029905811 Simplifying x + -0.04047599774 = -0.029905811 Reorder the terms: -0.04047599774 + x = -0.029905811 Solving -0.04047599774 + x = -0.029905811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04047599774' to each side of the equation. -0.04047599774 + 0.04047599774 + x = -0.029905811 + 0.04047599774 Combine like terms: -0.04047599774 + 0.04047599774 = 0.00000000000 0.00000000000 + x = -0.029905811 + 0.04047599774 x = -0.029905811 + 0.04047599774 Combine like terms: -0.029905811 + 0.04047599774 = 0.01057018674 x = 0.01057018674 Simplifying x = 0.01057018674Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.07038180874, 0.01057018674}
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