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Simplifying x2 + 1.01x + -0.013 = 0 Reorder the terms: -0.013 + 1.01x + x2 = 0 Solving -0.013 + 1.01x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.013' to each side of the equation. -0.013 + 1.01x + 0.013 + x2 = 0 + 0.013 Reorder the terms: -0.013 + 0.013 + 1.01x + x2 = 0 + 0.013 Combine like terms: -0.013 + 0.013 = 0.000 0.000 + 1.01x + x2 = 0 + 0.013 1.01x + x2 = 0 + 0.013 Combine like terms: 0 + 0.013 = 0.013 1.01x + x2 = 0.013 The x term is 1.01x. Take half its coefficient (0.505). Square it (0.255025) and add it to both sides. Add '0.255025' to each side of the equation. 1.01x + 0.255025 + x2 = 0.013 + 0.255025 Reorder the terms: 0.255025 + 1.01x + x2 = 0.013 + 0.255025 Combine like terms: 0.013 + 0.255025 = 0.268025 0.255025 + 1.01x + x2 = 0.268025 Factor a perfect square on the left side: (x + 0.505)(x + 0.505) = 0.268025 Calculate the square root of the right side: 0.51771131 Break this problem into two subproblems by setting (x + 0.505) equal to 0.51771131 and -0.51771131.Subproblem 1
x + 0.505 = 0.51771131 Simplifying x + 0.505 = 0.51771131 Reorder the terms: 0.505 + x = 0.51771131 Solving 0.505 + x = 0.51771131 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.505' to each side of the equation. 0.505 + -0.505 + x = 0.51771131 + -0.505 Combine like terms: 0.505 + -0.505 = 0.000 0.000 + x = 0.51771131 + -0.505 x = 0.51771131 + -0.505 Combine like terms: 0.51771131 + -0.505 = 0.01271131 x = 0.01271131 Simplifying x = 0.01271131Subproblem 2
x + 0.505 = -0.51771131 Simplifying x + 0.505 = -0.51771131 Reorder the terms: 0.505 + x = -0.51771131 Solving 0.505 + x = -0.51771131 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.505' to each side of the equation. 0.505 + -0.505 + x = -0.51771131 + -0.505 Combine like terms: 0.505 + -0.505 = 0.000 0.000 + x = -0.51771131 + -0.505 x = -0.51771131 + -0.505 Combine like terms: -0.51771131 + -0.505 = -1.02271131 x = -1.02271131 Simplifying x = -1.02271131Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.01271131, -1.02271131}
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