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Simplifying 0 = -1x2 + -1.8x + 30.6 Reorder the terms: 0 = 30.6 + -1.8x + -1x2 Solving 0 = 30.6 + -1.8x + -1x2 Solving for variable 'x'. Combine like terms: 0 + -30.6 = -30.6 -30.6 + 1.8x + x2 = 30.6 + -1.8x + -1x2 + -30.6 + 1.8x + x2 Reorder the terms: -30.6 + 1.8x + x2 = 30.6 + -30.6 + -1.8x + 1.8x + -1x2 + x2 Combine like terms: 30.6 + -30.6 = 0.0 -30.6 + 1.8x + x2 = 0.0 + -1.8x + 1.8x + -1x2 + x2 -30.6 + 1.8x + x2 = -1.8x + 1.8x + -1x2 + x2 Combine like terms: -1.8x + 1.8x = 0.0 -30.6 + 1.8x + x2 = 0.0 + -1x2 + x2 -30.6 + 1.8x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -30.6 + 1.8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '30.6' to each side of the equation. -30.6 + 1.8x + 30.6 + x2 = 0 + 30.6 Reorder the terms: -30.6 + 30.6 + 1.8x + x2 = 0 + 30.6 Combine like terms: -30.6 + 30.6 = 0.0 0.0 + 1.8x + x2 = 0 + 30.6 1.8x + x2 = 0 + 30.6 Combine like terms: 0 + 30.6 = 30.6 1.8x + x2 = 30.6 The x term is 1.8x. Take half its coefficient (0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. 1.8x + 0.81 + x2 = 30.6 + 0.81 Reorder the terms: 0.81 + 1.8x + x2 = 30.6 + 0.81 Combine like terms: 30.6 + 0.81 = 31.41 0.81 + 1.8x + x2 = 31.41 Factor a perfect square on the left side: (x + 0.9)(x + 0.9) = 31.41 Calculate the square root of the right side: 5.604462508 Break this problem into two subproblems by setting (x + 0.9) equal to 5.604462508 and -5.604462508.Subproblem 1
x + 0.9 = 5.604462508 Simplifying x + 0.9 = 5.604462508 Reorder the terms: 0.9 + x = 5.604462508 Solving 0.9 + x = 5.604462508 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = 5.604462508 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = 5.604462508 + -0.9 x = 5.604462508 + -0.9 Combine like terms: 5.604462508 + -0.9 = 4.704462508 x = 4.704462508 Simplifying x = 4.704462508Subproblem 2
x + 0.9 = -5.604462508 Simplifying x + 0.9 = -5.604462508 Reorder the terms: 0.9 + x = -5.604462508 Solving 0.9 + x = -5.604462508 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = -5.604462508 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = -5.604462508 + -0.9 x = -5.604462508 + -0.9 Combine like terms: -5.604462508 + -0.9 = -6.504462508 x = -6.504462508 Simplifying x = -6.504462508Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.704462508, -6.504462508}
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