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Simplifying 15x2 + 46x + -21 = 0 Reorder the terms: -21 + 46x + 15x2 = 0 Solving -21 + 46x + 15x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -1.4 + 3.066666667x + x2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + 3.066666667x + 1.4 + x2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + 3.066666667x + x2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + 3.066666667x + x2 = 0 + 1.4 3.066666667x + x2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 3.066666667x + x2 = 1.4 The x term is 3.066666667x. Take half its coefficient (1.533333334). Square it (2.351111113) and add it to both sides. Add '2.351111113' to each side of the equation. 3.066666667x + 2.351111113 + x2 = 1.4 + 2.351111113 Reorder the terms: 2.351111113 + 3.066666667x + x2 = 1.4 + 2.351111113 Combine like terms: 1.4 + 2.351111113 = 3.751111113 2.351111113 + 3.066666667x + x2 = 3.751111113 Factor a perfect square on the left side: (x + 1.533333334)(x + 1.533333334) = 3.751111113 Calculate the square root of the right side: 1.93677854 Break this problem into two subproblems by setting (x + 1.533333334) equal to 1.93677854 and -1.93677854.Subproblem 1
x + 1.533333334 = 1.93677854 Simplifying x + 1.533333334 = 1.93677854 Reorder the terms: 1.533333334 + x = 1.93677854 Solving 1.533333334 + x = 1.93677854 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.533333334' to each side of the equation. 1.533333334 + -1.533333334 + x = 1.93677854 + -1.533333334 Combine like terms: 1.533333334 + -1.533333334 = 0.000000000 0.000000000 + x = 1.93677854 + -1.533333334 x = 1.93677854 + -1.533333334 Combine like terms: 1.93677854 + -1.533333334 = 0.403445206 x = 0.403445206 Simplifying x = 0.403445206Subproblem 2
x + 1.533333334 = -1.93677854 Simplifying x + 1.533333334 = -1.93677854 Reorder the terms: 1.533333334 + x = -1.93677854 Solving 1.533333334 + x = -1.93677854 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.533333334' to each side of the equation. 1.533333334 + -1.533333334 + x = -1.93677854 + -1.533333334 Combine like terms: 1.533333334 + -1.533333334 = 0.000000000 0.000000000 + x = -1.93677854 + -1.533333334 x = -1.93677854 + -1.533333334 Combine like terms: -1.93677854 + -1.533333334 = -3.470111874 x = -3.470111874 Simplifying x = -3.470111874Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.403445206, -3.470111874}
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