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Simplifying 2.25x2 + 3x + -4 = 0 Reorder the terms: -4 + 3x + 2.25x2 = 0 Solving -4 + 3x + 2.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2.25 the coefficient of the squared term: Divide each side by '2.25'. -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 = 0.8240453185 x = 0.8240453185 Simplifying x = 0.8240453185Subproblem 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 = -2.1573786515 x = -2.1573786515 Simplifying x = -2.1573786515Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8240453185, -2.1573786515}
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