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Simplifying 1 + 0.75x + -0.5625x2 = 0 Solving 1 + 0.75x + -0.5625x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.5625 the coefficient of the squared term: Divide each side by '-0.5625'. -1.777777778 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '1.777777778' to each side of the equation. -1.777777778 + -1.333333333x + 1.777777778 + x2 = 0 + 1.777777778 Reorder the terms: -1.777777778 + 1.777777778 + -1.333333333x + x2 = 0 + 1.777777778 Combine like terms: -1.777777778 + 1.777777778 = 0.000000000 0.000000000 + -1.333333333x + x2 = 0 + 1.777777778 -1.333333333x + x2 = 0 + 1.777777778 Combine like terms: 0 + 1.777777778 = 1.777777778 -1.333333333x + x2 = 1.777777778 The x term is -1.333333333x. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333x + 0.4444444442 + x2 = 1.777777778 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = 1.777777778 + 0.4444444442 Combine like terms: 1.777777778 + 0.4444444442 = 2.2222222222 0.4444444442 + -1.333333333x + x2 = 2.2222222222 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = 2.2222222222 Calculate the square root of the right side: 1.490711985 Break this problem into two subproblems by setting (x + -0.6666666665) equal to 1.490711985 and -1.490711985.Subproblem 1
x + -0.6666666665 = 1.490711985 Simplifying x + -0.6666666665 = 1.490711985 Reorder the terms: -0.6666666665 + x = 1.490711985 Solving -0.6666666665 + x = 1.490711985 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = 1.490711985 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 1.490711985 + 0.6666666665 x = 1.490711985 + 0.6666666665 Combine like terms: 1.490711985 + 0.6666666665 = 2.1573786515 x = 2.1573786515 Simplifying x = 2.1573786515Subproblem 2
x + -0.6666666665 = -1.490711985 Simplifying x + -0.6666666665 = -1.490711985 Reorder the terms: -0.6666666665 + x = -1.490711985 Solving -0.6666666665 + x = -1.490711985 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = -1.490711985 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -1.490711985 + 0.6666666665 x = -1.490711985 + 0.6666666665 Combine like terms: -1.490711985 + 0.6666666665 = -0.8240453185 x = -0.8240453185 Simplifying x = -0.8240453185Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.1573786515, -0.8240453185}
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