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Simplifying 12x2 + 46x + 15 = 0 Reorder the terms: 15 + 46x + 12x2 = 0 Solving 15 + 46x + 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 + 3.833333333x + x2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + 3.833333333x + -1.25 + x2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + 3.833333333x + x2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + 3.833333333x + x2 = 0 + -1.25 3.833333333x + x2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 3.833333333x + x2 = -1.25 The x term is 3.833333333x. Take half its coefficient (1.916666667). Square it (3.673611112) and add it to both sides. Add '3.673611112' to each side of the equation. 3.833333333x + 3.673611112 + x2 = -1.25 + 3.673611112 Reorder the terms: 3.673611112 + 3.833333333x + x2 = -1.25 + 3.673611112 Combine like terms: -1.25 + 3.673611112 = 2.423611112 3.673611112 + 3.833333333x + x2 = 2.423611112 Factor a perfect square on the left side: (x + 1.916666667)(x + 1.916666667) = 2.423611112 Calculate the square root of the right side: 1.556795141 Break this problem into two subproblems by setting (x + 1.916666667) equal to 1.556795141 and -1.556795141.Subproblem 1
x + 1.916666667 = 1.556795141 Simplifying x + 1.916666667 = 1.556795141 Reorder the terms: 1.916666667 + x = 1.556795141 Solving 1.916666667 + x = 1.556795141 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.916666667' to each side of the equation. 1.916666667 + -1.916666667 + x = 1.556795141 + -1.916666667 Combine like terms: 1.916666667 + -1.916666667 = 0.000000000 0.000000000 + x = 1.556795141 + -1.916666667 x = 1.556795141 + -1.916666667 Combine like terms: 1.556795141 + -1.916666667 = -0.359871526 x = -0.359871526 Simplifying x = -0.359871526Subproblem 2
x + 1.916666667 = -1.556795141 Simplifying x + 1.916666667 = -1.556795141 Reorder the terms: 1.916666667 + x = -1.556795141 Solving 1.916666667 + x = -1.556795141 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.916666667' to each side of the equation. 1.916666667 + -1.916666667 + x = -1.556795141 + -1.916666667 Combine like terms: 1.916666667 + -1.916666667 = 0.000000000 0.000000000 + x = -1.556795141 + -1.916666667 x = -1.556795141 + -1.916666667 Combine like terms: -1.556795141 + -1.916666667 = -3.473461808 x = -3.473461808 Simplifying x = -3.473461808Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.359871526, -3.473461808}
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