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Simplifying 30x2 + 2000x + -230 = 0 Reorder the terms: -230 + 2000x + 30x2 = 0 Solving -230 + 2000x + 30x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '10'. 10(-23 + 200x + 3x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-23 + 200x + 3x2)' equal to zero and attempt to solve: Simplifying -23 + 200x + 3x2 = 0 Solving -23 + 200x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -7.666666667 + 66.66666667x + x2 = 0 Move the constant term to the right: Add '7.666666667' to each side of the equation. -7.666666667 + 66.66666667x + 7.666666667 + x2 = 0 + 7.666666667 Reorder the terms: -7.666666667 + 7.666666667 + 66.66666667x + x2 = 0 + 7.666666667 Combine like terms: -7.666666667 + 7.666666667 = 0.000000000 0.000000000 + 66.66666667x + x2 = 0 + 7.666666667 66.66666667x + x2 = 0 + 7.666666667 Combine like terms: 0 + 7.666666667 = 7.666666667 66.66666667x + x2 = 7.666666667 The x term is 66.66666667x. Take half its coefficient (33.33333334). Square it (1111.111112) and add it to both sides. Add '1111.111112' to each side of the equation. 66.66666667x + 1111.111112 + x2 = 7.666666667 + 1111.111112 Reorder the terms: 1111.111112 + 66.66666667x + x2 = 7.666666667 + 1111.111112 Combine like terms: 7.666666667 + 1111.111112 = 1118.777778667 1111.111112 + 66.66666667x + x2 = 1118.777778667 Factor a perfect square on the left side: (x + 33.33333334)(x + 33.33333334) = 1118.777778667 Calculate the square root of the right side: 33.448135653 Break this problem into two subproblems by setting (x + 33.33333334) equal to 33.448135653 and -33.448135653.Subproblem 1
x + 33.33333334 = 33.448135653 Simplifying x + 33.33333334 = 33.448135653 Reorder the terms: 33.33333334 + x = 33.448135653 Solving 33.33333334 + x = 33.448135653 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-33.33333334' to each side of the equation. 33.33333334 + -33.33333334 + x = 33.448135653 + -33.33333334 Combine like terms: 33.33333334 + -33.33333334 = 0.00000000 0.00000000 + x = 33.448135653 + -33.33333334 x = 33.448135653 + -33.33333334 Combine like terms: 33.448135653 + -33.33333334 = 0.114802313 x = 0.114802313 Simplifying x = 0.114802313Subproblem 2
x + 33.33333334 = -33.448135653 Simplifying x + 33.33333334 = -33.448135653 Reorder the terms: 33.33333334 + x = -33.448135653 Solving 33.33333334 + x = -33.448135653 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-33.33333334' to each side of the equation. 33.33333334 + -33.33333334 + x = -33.448135653 + -33.33333334 Combine like terms: 33.33333334 + -33.33333334 = 0.00000000 0.00000000 + x = -33.448135653 + -33.33333334 x = -33.448135653 + -33.33333334 Combine like terms: -33.448135653 + -33.33333334 = -66.781468993 x = -66.781468993 Simplifying x = -66.781468993Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.114802313, -66.781468993}Solution
x = {0.114802313, -66.781468993}
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