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Simplifying x2 + -15.19 = -1.8x Reorder the terms: -15.19 + x2 = -1.8x Solving -15.19 + x2 = -1.8x Solving for variable 'x'. Reorder the terms: -15.19 + 1.8x + x2 = -1.8x + 1.8x Combine like terms: -1.8x + 1.8x = 0.0 -15.19 + 1.8x + x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '15.19' to each side of the equation. -15.19 + 1.8x + 15.19 + x2 = 0.0 + 15.19 Reorder the terms: -15.19 + 15.19 + 1.8x + x2 = 0.0 + 15.19 Combine like terms: -15.19 + 15.19 = 0.00 0.00 + 1.8x + x2 = 0.0 + 15.19 1.8x + x2 = 0.0 + 15.19 Combine like terms: 0.0 + 15.19 = 15.19 1.8x + x2 = 15.19 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 = 15.19 + 0.81 Reorder the terms: 0.81 + 1.8x + x2 = 15.19 + 0.81 Combine like terms: 15.19 + 0.81 = 16 0.81 + 1.8x + x2 = 16 Factor a perfect square on the left side: (x + 0.9)(x + 0.9) = 16 Calculate the square root of the right side: 4 Break this problem into two subproblems by setting (x + 0.9) equal to 4 and -4.Subproblem 1
x + 0.9 = 4 Simplifying x + 0.9 = 4 Reorder the terms: 0.9 + x = 4 Solving 0.9 + x = 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 = 4 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = 4 + -0.9 x = 4 + -0.9 Combine like terms: 4 + -0.9 = 3.1 x = 3.1 Simplifying x = 3.1Subproblem 2
x + 0.9 = -4 Simplifying x + 0.9 = -4 Reorder the terms: 0.9 + x = -4 Solving 0.9 + x = -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 = -4 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = -4 + -0.9 x = -4 + -0.9 Combine like terms: -4 + -0.9 = -4.9 x = -4.9 Simplifying x = -4.9Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.1, -4.9}
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