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Simplifying x2 + x * 0.15 + -0.045 = 0 Reorder the terms for easier multiplication: x2 + 0.15x + -0.045 = 0 Reorder the terms: -0.045 + 0.15x + x2 = 0 Solving -0.045 + 0.15x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.045' to each side of the equation. -0.045 + 0.15x + 0.045 + x2 = 0 + 0.045 Reorder the terms: -0.045 + 0.045 + 0.15x + x2 = 0 + 0.045 Combine like terms: -0.045 + 0.045 = 0.000 0.000 + 0.15x + x2 = 0 + 0.045 0.15x + x2 = 0 + 0.045 Combine like terms: 0 + 0.045 = 0.045 0.15x + x2 = 0.045 The x term is 0.15x. Take half its coefficient (0.075). Square it (0.005625) and add it to both sides. Add '0.005625' to each side of the equation. 0.15x + 0.005625 + x2 = 0.045 + 0.005625 Reorder the terms: 0.005625 + 0.15x + x2 = 0.045 + 0.005625 Combine like terms: 0.045 + 0.005625 = 0.050625 0.005625 + 0.15x + x2 = 0.050625 Factor a perfect square on the left side: (x + 0.075)(x + 0.075) = 0.050625 Calculate the square root of the right side: 0.225 Break this problem into two subproblems by setting (x + 0.075) equal to 0.225 and -0.225.Subproblem 1
x + 0.075 = 0.225 Simplifying x + 0.075 = 0.225 Reorder the terms: 0.075 + x = 0.225 Solving 0.075 + x = 0.225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.075' to each side of the equation. 0.075 + -0.075 + x = 0.225 + -0.075 Combine like terms: 0.075 + -0.075 = 0.000 0.000 + x = 0.225 + -0.075 x = 0.225 + -0.075 Combine like terms: 0.225 + -0.075 = 0.15 x = 0.15 Simplifying x = 0.15Subproblem 2
x + 0.075 = -0.225 Simplifying x + 0.075 = -0.225 Reorder the terms: 0.075 + x = -0.225 Solving 0.075 + x = -0.225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.075' to each side of the equation. 0.075 + -0.075 + x = -0.225 + -0.075 Combine like terms: 0.075 + -0.075 = 0.000 0.000 + x = -0.225 + -0.075 x = -0.225 + -0.075 Combine like terms: -0.225 + -0.075 = -0.3 x = -0.3 Simplifying x = -0.3Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.15, -0.3}
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