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Simplifying x2 + 0.65 = 1.8x Reorder the terms: 0.65 + x2 = 1.8x Solving 0.65 + x2 = 1.8x Solving for variable 'x'. Reorder the terms: 0.65 + -1.8x + x2 = 1.8x + -1.8x Combine like terms: 1.8x + -1.8x = 0.0 0.65 + -1.8x + x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '-0.65' to each side of the equation. 0.65 + -1.8x + -0.65 + x2 = 0.0 + -0.65 Reorder the terms: 0.65 + -0.65 + -1.8x + x2 = 0.0 + -0.65 Combine like terms: 0.65 + -0.65 = 0.00 0.00 + -1.8x + x2 = 0.0 + -0.65 -1.8x + x2 = 0.0 + -0.65 Combine like terms: 0.0 + -0.65 = -0.65 -1.8x + x2 = -0.65 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 = -0.65 + 0.81 Reorder the terms: 0.81 + -1.8x + x2 = -0.65 + 0.81 Combine like terms: -0.65 + 0.81 = 0.16 0.81 + -1.8x + x2 = 0.16 Factor a perfect square on the left side: (x + -0.9)(x + -0.9) = 0.16 Calculate the square root of the right side: 0.4 Break this problem into two subproblems by setting (x + -0.9) equal to 0.4 and -0.4.Subproblem 1
x + -0.9 = 0.4 Simplifying x + -0.9 = 0.4 Reorder the terms: -0.9 + x = 0.4 Solving -0.9 + x = 0.4 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 = 0.4 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = 0.4 + 0.9 x = 0.4 + 0.9 Combine like terms: 0.4 + 0.9 = 1.3 x = 1.3 Simplifying x = 1.3Subproblem 2
x + -0.9 = -0.4 Simplifying x + -0.9 = -0.4 Reorder the terms: -0.9 + x = -0.4 Solving -0.9 + x = -0.4 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 = -0.4 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = -0.4 + 0.9 x = -0.4 + 0.9 Combine like terms: -0.4 + 0.9 = 0.5 x = 0.5 Simplifying x = 0.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3, 0.5}
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