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Simplifying x2 + 1.5x + -0.6 = 0 Reorder the terms: -0.6 + 1.5x + x2 = 0 Solving -0.6 + 1.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + 1.5x + 0.6 + x2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + 1.5x + x2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + 1.5x + x2 = 0 + 0.6 1.5x + x2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 1.5x + x2 = 0.6 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 0.6 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 0.6 + 0.5625 Combine like terms: 0.6 + 0.5625 = 1.1625 0.5625 + 1.5x + x2 = 1.1625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 1.1625 Calculate the square root of the right side: 1.078192933 Break this problem into two subproblems by setting (x + 0.75) equal to 1.078192933 and -1.078192933.Subproblem 1
x + 0.75 = 1.078192933 Simplifying x + 0.75 = 1.078192933 Reorder the terms: 0.75 + x = 1.078192933 Solving 0.75 + x = 1.078192933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 1.078192933 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 1.078192933 + -0.75 x = 1.078192933 + -0.75 Combine like terms: 1.078192933 + -0.75 = 0.328192933 x = 0.328192933 Simplifying x = 0.328192933Subproblem 2
x + 0.75 = -1.078192933 Simplifying x + 0.75 = -1.078192933 Reorder the terms: 0.75 + x = -1.078192933 Solving 0.75 + x = -1.078192933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -1.078192933 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -1.078192933 + -0.75 x = -1.078192933 + -0.75 Combine like terms: -1.078192933 + -0.75 = -1.828192933 x = -1.828192933 Simplifying x = -1.828192933Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.328192933, -1.828192933}
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