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Simplifying 10x2 + -36x + 2 = 0 Reorder the terms: 2 + -36x + 10x2 = 0 Solving 2 + -36x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + -18x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -18x + 5x2)' equal to zero and attempt to solve: Simplifying 1 + -18x + 5x2 = 0 Solving 1 + -18x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.2 + -3.6x + x2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + -3.6x + -0.2 + x2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + -3.6x + x2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + -3.6x + x2 = 0 + -0.2 -3.6x + x2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 -3.6x + x2 = -0.2 The x term is -3.6x. Take half its coefficient (-1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. -3.6x + 3.24 + x2 = -0.2 + 3.24 Reorder the terms: 3.24 + -3.6x + x2 = -0.2 + 3.24 Combine like terms: -0.2 + 3.24 = 3.04 3.24 + -3.6x + x2 = 3.04 Factor a perfect square on the left side: (x + -1.8)(x + -1.8) = 3.04 Calculate the square root of the right side: 1.743559577 Break this problem into two subproblems by setting (x + -1.8) equal to 1.743559577 and -1.743559577.Subproblem 1
x + -1.8 = 1.743559577 Simplifying x + -1.8 = 1.743559577 Reorder the terms: -1.8 + x = 1.743559577 Solving -1.8 + x = 1.743559577 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x = 1.743559577 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = 1.743559577 + 1.8 x = 1.743559577 + 1.8 Combine like terms: 1.743559577 + 1.8 = 3.543559577 x = 3.543559577 Simplifying x = 3.543559577Subproblem 2
x + -1.8 = -1.743559577 Simplifying x + -1.8 = -1.743559577 Reorder the terms: -1.8 + x = -1.743559577 Solving -1.8 + x = -1.743559577 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x = -1.743559577 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = -1.743559577 + 1.8 x = -1.743559577 + 1.8 Combine like terms: -1.743559577 + 1.8 = 0.056440423 x = 0.056440423 Simplifying x = 0.056440423Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.543559577, 0.056440423}Solution
x = {3.543559577, 0.056440423}
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