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Simplifying 15x2 + -12x + -20 = 0 Reorder the terms: -20 + -12x + 15x2 = 0 Solving -20 + -12x + 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'. -1.333333333 + -0.8x + x2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + -0.8x + 1.333333333 + x2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + -0.8x + x2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + -0.8x + x2 = 0 + 1.333333333 -0.8x + x2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 -0.8x + x2 = 1.333333333 The x term is -0.8x. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8x + 0.16 + x2 = 1.333333333 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = 1.333333333 + 0.16 Combine like terms: 1.333333333 + 0.16 = 1.493333333 0.16 + -0.8x + x2 = 1.493333333 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = 1.493333333 Calculate the square root of the right side: 1.222020185 Break this problem into two subproblems by setting (x + -0.4) equal to 1.222020185 and -1.222020185.Subproblem 1
x + -0.4 = 1.222020185 Simplifying x + -0.4 = 1.222020185 Reorder the terms: -0.4 + x = 1.222020185 Solving -0.4 + x = 1.222020185 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = 1.222020185 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 1.222020185 + 0.4 x = 1.222020185 + 0.4 Combine like terms: 1.222020185 + 0.4 = 1.622020185 x = 1.622020185 Simplifying x = 1.622020185Subproblem 2
x + -0.4 = -1.222020185 Simplifying x + -0.4 = -1.222020185 Reorder the terms: -0.4 + x = -1.222020185 Solving -0.4 + x = -1.222020185 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = -1.222020185 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -1.222020185 + 0.4 x = -1.222020185 + 0.4 Combine like terms: -1.222020185 + 0.4 = -0.822020185 x = -0.822020185 Simplifying x = -0.822020185Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.622020185, -0.822020185}
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