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Simplifying x2 + -1.9x + 0.7 = 0 Reorder the terms: 0.7 + -1.9x + x2 = 0 Solving 0.7 + -1.9x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.7' to each side of the equation. 0.7 + -1.9x + -0.7 + x2 = 0 + -0.7 Reorder the terms: 0.7 + -0.7 + -1.9x + x2 = 0 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + -1.9x + x2 = 0 + -0.7 -1.9x + x2 = 0 + -0.7 Combine like terms: 0 + -0.7 = -0.7 -1.9x + x2 = -0.7 The x term is -1.9x. Take half its coefficient (-0.95). Square it (0.9025) and add it to both sides. Add '0.9025' to each side of the equation. -1.9x + 0.9025 + x2 = -0.7 + 0.9025 Reorder the terms: 0.9025 + -1.9x + x2 = -0.7 + 0.9025 Combine like terms: -0.7 + 0.9025 = 0.2025 0.9025 + -1.9x + x2 = 0.2025 Factor a perfect square on the left side: (x + -0.95)(x + -0.95) = 0.2025 Calculate the square root of the right side: 0.45 Break this problem into two subproblems by setting (x + -0.95) equal to 0.45 and -0.45.Subproblem 1
x + -0.95 = 0.45 Simplifying x + -0.95 = 0.45 Reorder the terms: -0.95 + x = 0.45 Solving -0.95 + x = 0.45 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.95' to each side of the equation. -0.95 + 0.95 + x = 0.45 + 0.95 Combine like terms: -0.95 + 0.95 = 0.00 0.00 + x = 0.45 + 0.95 x = 0.45 + 0.95 Combine like terms: 0.45 + 0.95 = 1.4 x = 1.4 Simplifying x = 1.4Subproblem 2
x + -0.95 = -0.45 Simplifying x + -0.95 = -0.45 Reorder the terms: -0.95 + x = -0.45 Solving -0.95 + x = -0.45 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.95' to each side of the equation. -0.95 + 0.95 + x = -0.45 + 0.95 Combine like terms: -0.95 + 0.95 = 0.00 0.00 + x = -0.45 + 0.95 x = -0.45 + 0.95 Combine like terms: -0.45 + 0.95 = 0.5 x = 0.5 Simplifying x = 0.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4, 0.5}
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