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Simplifying 15x2 + 14x + -3 = 0 Reorder the terms: -3 + 14x + 15x2 = 0 Solving -3 + 14x + 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'. -0.2 + 0.9333333333x + x2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + 0.9333333333x + 0.2 + x2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + 0.9333333333x + x2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + 0.9333333333x + x2 = 0 + 0.2 0.9333333333x + x2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 0.9333333333x + x2 = 0.2 The x term is 0.9333333333x. Take half its coefficient (0.4666666667). Square it (0.2177777778) and add it to both sides. Add '0.2177777778' to each side of the equation. 0.9333333333x + 0.2177777778 + x2 = 0.2 + 0.2177777778 Reorder the terms: 0.2177777778 + 0.9333333333x + x2 = 0.2 + 0.2177777778 Combine like terms: 0.2 + 0.2177777778 = 0.4177777778 0.2177777778 + 0.9333333333x + x2 = 0.4177777778 Factor a perfect square on the left side: (x + 0.4666666667)(x + 0.4666666667) = 0.4177777778 Calculate the square root of the right side: 0.646357314 Break this problem into two subproblems by setting (x + 0.4666666667) equal to 0.646357314 and -0.646357314.Subproblem 1
x + 0.4666666667 = 0.646357314 Simplifying x + 0.4666666667 = 0.646357314 Reorder the terms: 0.4666666667 + x = 0.646357314 Solving 0.4666666667 + x = 0.646357314 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4666666667' to each side of the equation. 0.4666666667 + -0.4666666667 + x = 0.646357314 + -0.4666666667 Combine like terms: 0.4666666667 + -0.4666666667 = 0.0000000000 0.0000000000 + x = 0.646357314 + -0.4666666667 x = 0.646357314 + -0.4666666667 Combine like terms: 0.646357314 + -0.4666666667 = 0.1796906473 x = 0.1796906473 Simplifying x = 0.1796906473Subproblem 2
x + 0.4666666667 = -0.646357314 Simplifying x + 0.4666666667 = -0.646357314 Reorder the terms: 0.4666666667 + x = -0.646357314 Solving 0.4666666667 + x = -0.646357314 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4666666667' to each side of the equation. 0.4666666667 + -0.4666666667 + x = -0.646357314 + -0.4666666667 Combine like terms: 0.4666666667 + -0.4666666667 = 0.0000000000 0.0000000000 + x = -0.646357314 + -0.4666666667 x = -0.646357314 + -0.4666666667 Combine like terms: -0.646357314 + -0.4666666667 = -1.1130239807 x = -1.1130239807 Simplifying x = -1.1130239807Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1796906473, -1.1130239807}
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