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Simplifying x2 + 0.03x + -0.91 = 0 Reorder the terms: -0.91 + 0.03x + x2 = 0 Solving -0.91 + 0.03x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.91' to each side of the equation. -0.91 + 0.03x + 0.91 + x2 = 0 + 0.91 Reorder the terms: -0.91 + 0.91 + 0.03x + x2 = 0 + 0.91 Combine like terms: -0.91 + 0.91 = 0.00 0.00 + 0.03x + x2 = 0 + 0.91 0.03x + x2 = 0 + 0.91 Combine like terms: 0 + 0.91 = 0.91 0.03x + x2 = 0.91 The x term is 0.03x. Take half its coefficient (0.015). Square it (0.000225) and add it to both sides. Add '0.000225' to each side of the equation. 0.03x + 0.000225 + x2 = 0.91 + 0.000225 Reorder the terms: 0.000225 + 0.03x + x2 = 0.91 + 0.000225 Combine like terms: 0.91 + 0.000225 = 0.910225 0.000225 + 0.03x + x2 = 0.910225 Factor a perfect square on the left side: (x + 0.015)(x + 0.015) = 0.910225 Calculate the square root of the right side: 0.954057126 Break this problem into two subproblems by setting (x + 0.015) equal to 0.954057126 and -0.954057126.Subproblem 1
x + 0.015 = 0.954057126 Simplifying x + 0.015 = 0.954057126 Reorder the terms: 0.015 + x = 0.954057126 Solving 0.015 + x = 0.954057126 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.015' to each side of the equation. 0.015 + -0.015 + x = 0.954057126 + -0.015 Combine like terms: 0.015 + -0.015 = 0.000 0.000 + x = 0.954057126 + -0.015 x = 0.954057126 + -0.015 Combine like terms: 0.954057126 + -0.015 = 0.939057126 x = 0.939057126 Simplifying x = 0.939057126Subproblem 2
x + 0.015 = -0.954057126 Simplifying x + 0.015 = -0.954057126 Reorder the terms: 0.015 + x = -0.954057126 Solving 0.015 + x = -0.954057126 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.015' to each side of the equation. 0.015 + -0.015 + x = -0.954057126 + -0.015 Combine like terms: 0.015 + -0.015 = 0.000 0.000 + x = -0.954057126 + -0.015 x = -0.954057126 + -0.015 Combine like terms: -0.954057126 + -0.015 = -0.969057126 x = -0.969057126 Simplifying x = -0.969057126Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.939057126, -0.969057126}
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