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Simplifying x2 + 0.15x + -0.45 = 0 Reorder the terms: -0.45 + 0.15x + x2 = 0 Solving -0.45 + 0.15x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.45' to each side of the equation. -0.45 + 0.15x + 0.45 + x2 = 0 + 0.45 Reorder the terms: -0.45 + 0.45 + 0.15x + x2 = 0 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + 0.15x + x2 = 0 + 0.45 0.15x + x2 = 0 + 0.45 Combine like terms: 0 + 0.45 = 0.45 0.15x + x2 = 0.45 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 = 0.45 + 0.005625 Reorder the terms: 0.005625 + 0.15x + x2 = 0.45 + 0.005625 Combine like terms: 0.45 + 0.005625 = 0.455625 0.005625 + 0.15x + x2 = 0.455625 Factor a perfect square on the left side: (x + 0.075)(x + 0.075) = 0.455625 Calculate the square root of the right side: 0.675 Break this problem into two subproblems by setting (x + 0.075) equal to 0.675 and -0.675.Subproblem 1
x + 0.075 = 0.675 Simplifying x + 0.075 = 0.675 Reorder the terms: 0.075 + x = 0.675 Solving 0.075 + x = 0.675 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 = 0.675 + -0.075 Combine like terms: 0.075 + -0.075 = 0.000 0.000 + x = 0.675 + -0.075 x = 0.675 + -0.075 Combine like terms: 0.675 + -0.075 = 0.6 x = 0.6 Simplifying x = 0.6Subproblem 2
x + 0.075 = -0.675 Simplifying x + 0.075 = -0.675 Reorder the terms: 0.075 + x = -0.675 Solving 0.075 + x = -0.675 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 = -0.675 + -0.075 Combine like terms: 0.075 + -0.075 = 0.000 0.000 + x = -0.675 + -0.075 x = -0.675 + -0.075 Combine like terms: -0.675 + -0.075 = -0.75 x = -0.75 Simplifying x = -0.75Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6, -0.75}
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