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Simplifying 12x2 + -28x + -15 = 0 Reorder the terms: -15 + -28x + 12x2 = 0 Solving -15 + -28x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -1.25 + -2.333333333x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -2.333333333x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -2.333333333x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -2.333333333x + x2 = 0 + 1.25 -2.333333333x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -2.333333333x + x2 = 1.25 The x term is -2.333333333x. Take half its coefficient (-1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. -2.333333333x + 1.361111112 + x2 = 1.25 + 1.361111112 Reorder the terms: 1.361111112 + -2.333333333x + x2 = 1.25 + 1.361111112 Combine like terms: 1.25 + 1.361111112 = 2.611111112 1.361111112 + -2.333333333x + x2 = 2.611111112 Factor a perfect square on the left side: (x + -1.166666667)(x + -1.166666667) = 2.611111112 Calculate the square root of the right side: 1.615893286 Break this problem into two subproblems by setting (x + -1.166666667) equal to 1.615893286 and -1.615893286.Subproblem 1
x + -1.166666667 = 1.615893286 Simplifying x + -1.166666667 = 1.615893286 Reorder the terms: -1.166666667 + x = 1.615893286 Solving -1.166666667 + x = 1.615893286 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + x = 1.615893286 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = 1.615893286 + 1.166666667 x = 1.615893286 + 1.166666667 Combine like terms: 1.615893286 + 1.166666667 = 2.782559953 x = 2.782559953 Simplifying x = 2.782559953Subproblem 2
x + -1.166666667 = -1.615893286 Simplifying x + -1.166666667 = -1.615893286 Reorder the terms: -1.166666667 + x = -1.615893286 Solving -1.166666667 + x = -1.615893286 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + x = -1.615893286 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = -1.615893286 + 1.166666667 x = -1.615893286 + 1.166666667 Combine like terms: -1.615893286 + 1.166666667 = -0.449226619 x = -0.449226619 Simplifying x = -0.449226619Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.782559953, -0.449226619}
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