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Simplifying x2 + -1.5x + -1.43 = 0 Reorder the terms: -1.43 + -1.5x + x2 = 0 Solving -1.43 + -1.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1.43' to each side of the equation. -1.43 + -1.5x + 1.43 + x2 = 0 + 1.43 Reorder the terms: -1.43 + 1.43 + -1.5x + x2 = 0 + 1.43 Combine like terms: -1.43 + 1.43 = 0.00 0.00 + -1.5x + x2 = 0 + 1.43 -1.5x + x2 = 0 + 1.43 Combine like terms: 0 + 1.43 = 1.43 -1.5x + x2 = 1.43 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 = 1.43 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 1.43 + 0.5625 Combine like terms: 1.43 + 0.5625 = 1.9925 0.5625 + -1.5x + x2 = 1.9925 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 1.9925 Calculate the square root of the right side: 1.411559421 Break this problem into two subproblems by setting (x + -0.75) equal to 1.411559421 and -1.411559421.Subproblem 1
x + -0.75 = 1.411559421 Simplifying x + -0.75 = 1.411559421 Reorder the terms: -0.75 + x = 1.411559421 Solving -0.75 + x = 1.411559421 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 = 1.411559421 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 1.411559421 + 0.75 x = 1.411559421 + 0.75 Combine like terms: 1.411559421 + 0.75 = 2.161559421 x = 2.161559421 Simplifying x = 2.161559421Subproblem 2
x + -0.75 = -1.411559421 Simplifying x + -0.75 = -1.411559421 Reorder the terms: -0.75 + x = -1.411559421 Solving -0.75 + x = -1.411559421 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 = -1.411559421 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -1.411559421 + 0.75 x = -1.411559421 + 0.75 Combine like terms: -1.411559421 + 0.75 = -0.661559421 x = -0.661559421 Simplifying x = -0.661559421Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.161559421, -0.661559421}
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