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Simplifying 39000x2 + -63000x + 12000 = 0 Reorder the terms: 12000 + -63000x + 39000x2 = 0 Solving 12000 + -63000x + 39000x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3000'. 3000(4 + -21x + 13x2) = 0 Ignore the factor 3000.Subproblem 1
Set the factor '(4 + -21x + 13x2)' equal to zero and attempt to solve: Simplifying 4 + -21x + 13x2 = 0 Solving 4 + -21x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. 0.3076923077 + -1.615384615x + x2 = 0 Move the constant term to the right: Add '-0.3076923077' to each side of the equation. 0.3076923077 + -1.615384615x + -0.3076923077 + x2 = 0 + -0.3076923077 Reorder the terms: 0.3076923077 + -0.3076923077 + -1.615384615x + x2 = 0 + -0.3076923077 Combine like terms: 0.3076923077 + -0.3076923077 = 0.0000000000 0.0000000000 + -1.615384615x + x2 = 0 + -0.3076923077 -1.615384615x + x2 = 0 + -0.3076923077 Combine like terms: 0 + -0.3076923077 = -0.3076923077 -1.615384615x + x2 = -0.3076923077 The x term is -1.615384615x. Take half its coefficient (-0.8076923075). Square it (0.6523668636) and add it to both sides. Add '0.6523668636' to each side of the equation. -1.615384615x + 0.6523668636 + x2 = -0.3076923077 + 0.6523668636 Reorder the terms: 0.6523668636 + -1.615384615x + x2 = -0.3076923077 + 0.6523668636 Combine like terms: -0.3076923077 + 0.6523668636 = 0.3446745559 0.6523668636 + -1.615384615x + x2 = 0.3446745559 Factor a perfect square on the left side: (x + -0.8076923075)(x + -0.8076923075) = 0.3446745559 Calculate the square root of the right side: 0.587089904 Break this problem into two subproblems by setting (x + -0.8076923075) equal to 0.587089904 and -0.587089904.Subproblem 1
x + -0.8076923075 = 0.587089904 Simplifying x + -0.8076923075 = 0.587089904 Reorder the terms: -0.8076923075 + x = 0.587089904 Solving -0.8076923075 + x = 0.587089904 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8076923075' to each side of the equation. -0.8076923075 + 0.8076923075 + x = 0.587089904 + 0.8076923075 Combine like terms: -0.8076923075 + 0.8076923075 = 0.0000000000 0.0000000000 + x = 0.587089904 + 0.8076923075 x = 0.587089904 + 0.8076923075 Combine like terms: 0.587089904 + 0.8076923075 = 1.3947822115 x = 1.3947822115 Simplifying x = 1.3947822115Subproblem 2
x + -0.8076923075 = -0.587089904 Simplifying x + -0.8076923075 = -0.587089904 Reorder the terms: -0.8076923075 + x = -0.587089904 Solving -0.8076923075 + x = -0.587089904 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8076923075' to each side of the equation. -0.8076923075 + 0.8076923075 + x = -0.587089904 + 0.8076923075 Combine like terms: -0.8076923075 + 0.8076923075 = 0.0000000000 0.0000000000 + x = -0.587089904 + 0.8076923075 x = -0.587089904 + 0.8076923075 Combine like terms: -0.587089904 + 0.8076923075 = 0.2206024035 x = 0.2206024035 Simplifying x = 0.2206024035Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3947822115, 0.2206024035}Solution
x = {1.3947822115, 0.2206024035}
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