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Simplifying 18x2 + 3 + -53x = 0 Reorder the terms: 3 + -53x + 18x2 = 0 Solving 3 + -53x + 18x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. 0.1666666667 + -2.944444444x + x2 = 0 Move the constant term to the right: Add '-0.1666666667' to each side of the equation. 0.1666666667 + -2.944444444x + -0.1666666667 + x2 = 0 + -0.1666666667 Reorder the terms: 0.1666666667 + -0.1666666667 + -2.944444444x + x2 = 0 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + -2.944444444x + x2 = 0 + -0.1666666667 -2.944444444x + x2 = 0 + -0.1666666667 Combine like terms: 0 + -0.1666666667 = -0.1666666667 -2.944444444x + x2 = -0.1666666667 The x term is -2.944444444x. Take half its coefficient (-1.472222222). Square it (2.167438271) and add it to both sides. Add '2.167438271' to each side of the equation. -2.944444444x + 2.167438271 + x2 = -0.1666666667 + 2.167438271 Reorder the terms: 2.167438271 + -2.944444444x + x2 = -0.1666666667 + 2.167438271 Combine like terms: -0.1666666667 + 2.167438271 = 2.0007716043 2.167438271 + -2.944444444x + x2 = 2.0007716043 Factor a perfect square on the left side: (x + -1.472222222)(x + -1.472222222) = 2.0007716043 Calculate the square root of the right side: 1.414486339 Break this problem into two subproblems by setting (x + -1.472222222) equal to 1.414486339 and -1.414486339.Subproblem 1
x + -1.472222222 = 1.414486339 Simplifying x + -1.472222222 = 1.414486339 Reorder the terms: -1.472222222 + x = 1.414486339 Solving -1.472222222 + x = 1.414486339 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.472222222' to each side of the equation. -1.472222222 + 1.472222222 + x = 1.414486339 + 1.472222222 Combine like terms: -1.472222222 + 1.472222222 = 0.000000000 0.000000000 + x = 1.414486339 + 1.472222222 x = 1.414486339 + 1.472222222 Combine like terms: 1.414486339 + 1.472222222 = 2.886708561 x = 2.886708561 Simplifying x = 2.886708561Subproblem 2
x + -1.472222222 = -1.414486339 Simplifying x + -1.472222222 = -1.414486339 Reorder the terms: -1.472222222 + x = -1.414486339 Solving -1.472222222 + x = -1.414486339 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.472222222' to each side of the equation. -1.472222222 + 1.472222222 + x = -1.414486339 + 1.472222222 Combine like terms: -1.472222222 + 1.472222222 = 0.000000000 0.000000000 + x = -1.414486339 + 1.472222222 x = -1.414486339 + 1.472222222 Combine like terms: -1.414486339 + 1.472222222 = 0.057735883 x = 0.057735883 Simplifying x = 0.057735883Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.886708561, 0.057735883}
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