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Simplifying x2 + 1.8x + 0.81 = 31.36 Reorder the terms: 0.81 + 1.8x + x2 = 31.36 Solving 0.81 + 1.8x + x2 = 31.36 Solving for variable 'x'. Reorder the terms: 0.81 + -31.36 + 1.8x + x2 = 31.36 + -31.36 Combine like terms: 0.81 + -31.36 = -30.55 -30.55 + 1.8x + x2 = 31.36 + -31.36 Combine like terms: 31.36 + -31.36 = 0.00 -30.55 + 1.8x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '30.55' to each side of the equation. -30.55 + 1.8x + 30.55 + x2 = 0.00 + 30.55 Reorder the terms: -30.55 + 30.55 + 1.8x + x2 = 0.00 + 30.55 Combine like terms: -30.55 + 30.55 = 0.00 0.00 + 1.8x + x2 = 0.00 + 30.55 1.8x + x2 = 0.00 + 30.55 Combine like terms: 0.00 + 30.55 = 30.55 1.8x + x2 = 30.55 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 = 30.55 + 0.81 Reorder the terms: 0.81 + 1.8x + x2 = 30.55 + 0.81 Combine like terms: 30.55 + 0.81 = 31.36 0.81 + 1.8x + x2 = 31.36 Factor a perfect square on the left side: (x + 0.9)(x + 0.9) = 31.36 Calculate the square root of the right side: 5.6 Break this problem into two subproblems by setting (x + 0.9) equal to 5.6 and -5.6.Subproblem 1
x + 0.9 = 5.6 Simplifying x + 0.9 = 5.6 Reorder the terms: 0.9 + x = 5.6 Solving 0.9 + x = 5.6 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 = 5.6 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = 5.6 + -0.9 x = 5.6 + -0.9 Combine like terms: 5.6 + -0.9 = 4.7 x = 4.7 Simplifying x = 4.7Subproblem 2
x + 0.9 = -5.6 Simplifying x + 0.9 = -5.6 Reorder the terms: 0.9 + x = -5.6 Solving 0.9 + x = -5.6 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 = -5.6 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = -5.6 + -0.9 x = -5.6 + -0.9 Combine like terms: -5.6 + -0.9 = -6.5 x = -6.5 Simplifying x = -6.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.7, -6.5}
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