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Simplifying 3x2 + -19x = 63 Reorder the terms: -19x + 3x2 = 63 Solving -19x + 3x2 = 63 Solving for variable 'x'. Reorder the terms: -63 + -19x + 3x2 = 63 + -63 Combine like terms: 63 + -63 = 0 -63 + -19x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -21 + -6.333333333x + x2 = 0 Move the constant term to the right: Add '21' to each side of the equation. -21 + -6.333333333x + 21 + x2 = 0 + 21 Reorder the terms: -21 + 21 + -6.333333333x + x2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -6.333333333x + x2 = 0 + 21 -6.333333333x + x2 = 0 + 21 Combine like terms: 0 + 21 = 21 -6.333333333x + x2 = 21 The x term is -6.333333333x. Take half its coefficient (-3.166666667). Square it (10.02777778) and add it to both sides. Add '10.02777778' to each side of the equation. -6.333333333x + 10.02777778 + x2 = 21 + 10.02777778 Reorder the terms: 10.02777778 + -6.333333333x + x2 = 21 + 10.02777778 Combine like terms: 21 + 10.02777778 = 31.02777778 10.02777778 + -6.333333333x + x2 = 31.02777778 Factor a perfect square on the left side: (x + -3.166666667)(x + -3.166666667) = 31.02777778 Calculate the square root of the right side: 5.570258323 Break this problem into two subproblems by setting (x + -3.166666667) equal to 5.570258323 and -5.570258323.Subproblem 1
x + -3.166666667 = 5.570258323 Simplifying x + -3.166666667 = 5.570258323 Reorder the terms: -3.166666667 + x = 5.570258323 Solving -3.166666667 + x = 5.570258323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.166666667' to each side of the equation. -3.166666667 + 3.166666667 + x = 5.570258323 + 3.166666667 Combine like terms: -3.166666667 + 3.166666667 = 0.000000000 0.000000000 + x = 5.570258323 + 3.166666667 x = 5.570258323 + 3.166666667 Combine like terms: 5.570258323 + 3.166666667 = 8.73692499 x = 8.73692499 Simplifying x = 8.73692499Subproblem 2
x + -3.166666667 = -5.570258323 Simplifying x + -3.166666667 = -5.570258323 Reorder the terms: -3.166666667 + x = -5.570258323 Solving -3.166666667 + x = -5.570258323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.166666667' to each side of the equation. -3.166666667 + 3.166666667 + x = -5.570258323 + 3.166666667 Combine like terms: -3.166666667 + 3.166666667 = 0.000000000 0.000000000 + x = -5.570258323 + 3.166666667 x = -5.570258323 + 3.166666667 Combine like terms: -5.570258323 + 3.166666667 = -2.403591656 x = -2.403591656 Simplifying x = -2.403591656Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.73692499, -2.403591656}
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