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Simplifying x2 + 1.8x + -0.36 = 0 Reorder the terms: -0.36 + 1.8x + x2 = 0 Solving -0.36 + 1.8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.36' to each side of the equation. -0.36 + 1.8x + 0.36 + x2 = 0 + 0.36 Reorder the terms: -0.36 + 0.36 + 1.8x + x2 = 0 + 0.36 Combine like terms: -0.36 + 0.36 = 0.00 0.00 + 1.8x + x2 = 0 + 0.36 1.8x + x2 = 0 + 0.36 Combine like terms: 0 + 0.36 = 0.36 1.8x + x2 = 0.36 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 = 0.36 + 0.81 Reorder the terms: 0.81 + 1.8x + x2 = 0.36 + 0.81 Combine like terms: 0.36 + 0.81 = 1.17 0.81 + 1.8x + x2 = 1.17 Factor a perfect square on the left side: (x + 0.9)(x + 0.9) = 1.17 Calculate the square root of the right side: 1.081665383 Break this problem into two subproblems by setting (x + 0.9) equal to 1.081665383 and -1.081665383.Subproblem 1
x + 0.9 = 1.081665383 Simplifying x + 0.9 = 1.081665383 Reorder the terms: 0.9 + x = 1.081665383 Solving 0.9 + x = 1.081665383 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 = 1.081665383 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = 1.081665383 + -0.9 x = 1.081665383 + -0.9 Combine like terms: 1.081665383 + -0.9 = 0.181665383 x = 0.181665383 Simplifying x = 0.181665383Subproblem 2
x + 0.9 = -1.081665383 Simplifying x + 0.9 = -1.081665383 Reorder the terms: 0.9 + x = -1.081665383 Solving 0.9 + x = -1.081665383 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 = -1.081665383 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = -1.081665383 + -0.9 x = -1.081665383 + -0.9 Combine like terms: -1.081665383 + -0.9 = -1.981665383 x = -1.981665383 Simplifying x = -1.981665383Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.181665383, -1.981665383}
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