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Simplifying x2 + -1.8x + -4.95 = 0 Reorder the terms: -4.95 + -1.8x + x2 = 0 Solving -4.95 + -1.8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '4.95' to each side of the equation. -4.95 + -1.8x + 4.95 + x2 = 0 + 4.95 Reorder the terms: -4.95 + 4.95 + -1.8x + x2 = 0 + 4.95 Combine like terms: -4.95 + 4.95 = 0.00 0.00 + -1.8x + x2 = 0 + 4.95 -1.8x + x2 = 0 + 4.95 Combine like terms: 0 + 4.95 = 4.95 -1.8x + x2 = 4.95 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 = 4.95 + 0.81 Reorder the terms: 0.81 + -1.8x + x2 = 4.95 + 0.81 Combine like terms: 4.95 + 0.81 = 5.76 0.81 + -1.8x + x2 = 5.76 Factor a perfect square on the left side: (x + -0.9)(x + -0.9) = 5.76 Calculate the square root of the right side: 2.4 Break this problem into two subproblems by setting (x + -0.9) equal to 2.4 and -2.4.Subproblem 1
x + -0.9 = 2.4 Simplifying x + -0.9 = 2.4 Reorder the terms: -0.9 + x = 2.4 Solving -0.9 + x = 2.4 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 = 2.4 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = 2.4 + 0.9 x = 2.4 + 0.9 Combine like terms: 2.4 + 0.9 = 3.3 x = 3.3 Simplifying x = 3.3Subproblem 2
x + -0.9 = -2.4 Simplifying x + -0.9 = -2.4 Reorder the terms: -0.9 + x = -2.4 Solving -0.9 + x = -2.4 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 = -2.4 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = -2.4 + 0.9 x = -2.4 + 0.9 Combine like terms: -2.4 + 0.9 = -1.5 x = -1.5 Simplifying x = -1.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.3, -1.5}
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