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Simplifying 3x2 + -11x = 15 Reorder the terms: -11x + 3x2 = 15 Solving -11x + 3x2 = 15 Solving for variable 'x'. Reorder the terms: -15 + -11x + 3x2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + -11x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -5 + -3.666666667x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -3.666666667x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -3.666666667x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -3.666666667x + x2 = 0 + 5 -3.666666667x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -3.666666667x + x2 = 5 The x term is -3.666666667x. Take half its coefficient (-1.833333334). Square it (3.361111114) and add it to both sides. Add '3.361111114' to each side of the equation. -3.666666667x + 3.361111114 + x2 = 5 + 3.361111114 Reorder the terms: 3.361111114 + -3.666666667x + x2 = 5 + 3.361111114 Combine like terms: 5 + 3.361111114 = 8.361111114 3.361111114 + -3.666666667x + x2 = 8.361111114 Factor a perfect square on the left side: (x + -1.833333334)(x + -1.833333334) = 8.361111114 Calculate the square root of the right side: 2.891558596 Break this problem into two subproblems by setting (x + -1.833333334) equal to 2.891558596 and -2.891558596.Subproblem 1
x + -1.833333334 = 2.891558596 Simplifying x + -1.833333334 = 2.891558596 Reorder the terms: -1.833333334 + x = 2.891558596 Solving -1.833333334 + x = 2.891558596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + x = 2.891558596 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = 2.891558596 + 1.833333334 x = 2.891558596 + 1.833333334 Combine like terms: 2.891558596 + 1.833333334 = 4.72489193 x = 4.72489193 Simplifying x = 4.72489193Subproblem 2
x + -1.833333334 = -2.891558596 Simplifying x + -1.833333334 = -2.891558596 Reorder the terms: -1.833333334 + x = -2.891558596 Solving -1.833333334 + x = -2.891558596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + x = -2.891558596 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = -2.891558596 + 1.833333334 x = -2.891558596 + 1.833333334 Combine like terms: -2.891558596 + 1.833333334 = -1.058225262 x = -1.058225262 Simplifying x = -1.058225262Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.72489193, -1.058225262}
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