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Simplifying -15x2 + 12x + 28 = 0 Reorder the terms: 28 + 12x + -15x2 = 0 Solving 28 + 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'. -1.866666667 + -0.8x + x2 = 0 Move the constant term to the right: Add '1.866666667' to each side of the equation. -1.866666667 + -0.8x + 1.866666667 + x2 = 0 + 1.866666667 Reorder the terms: -1.866666667 + 1.866666667 + -0.8x + x2 = 0 + 1.866666667 Combine like terms: -1.866666667 + 1.866666667 = 0.000000000 0.000000000 + -0.8x + x2 = 0 + 1.866666667 -0.8x + x2 = 0 + 1.866666667 Combine like terms: 0 + 1.866666667 = 1.866666667 -0.8x + x2 = 1.866666667 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 = 1.866666667 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = 1.866666667 + 0.16 Combine like terms: 1.866666667 + 0.16 = 2.026666667 0.16 + -0.8x + x2 = 2.026666667 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = 2.026666667 Calculate the square root of the right side: 1.423610434 Break this problem into two subproblems by setting (x + -0.4) equal to 1.423610434 and -1.423610434.Subproblem 1
x + -0.4 = 1.423610434 Simplifying x + -0.4 = 1.423610434 Reorder the terms: -0.4 + x = 1.423610434 Solving -0.4 + x = 1.423610434 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 = 1.423610434 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 1.423610434 + 0.4 x = 1.423610434 + 0.4 Combine like terms: 1.423610434 + 0.4 = 1.823610434 x = 1.823610434 Simplifying x = 1.823610434Subproblem 2
x + -0.4 = -1.423610434 Simplifying x + -0.4 = -1.423610434 Reorder the terms: -0.4 + x = -1.423610434 Solving -0.4 + x = -1.423610434 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 = -1.423610434 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -1.423610434 + 0.4 x = -1.423610434 + 0.4 Combine like terms: -1.423610434 + 0.4 = -1.023610434 x = -1.023610434 Simplifying x = -1.023610434Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.823610434, -1.023610434}
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