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Simplifying 10 + 12x + -1.5x2 = 0 Solving 10 + 12x + -1.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1.5 the coefficient of the squared term: Divide each side by '-1.5'. -6.666666667 + -8x + x2 = 0 Move the constant term to the right: Add '6.666666667' to each side of the equation. -6.666666667 + -8x + 6.666666667 + x2 = 0 + 6.666666667 Reorder the terms: -6.666666667 + 6.666666667 + -8x + x2 = 0 + 6.666666667 Combine like terms: -6.666666667 + 6.666666667 = 0.000000000 0.000000000 + -8x + x2 = 0 + 6.666666667 -8x + x2 = 0 + 6.666666667 Combine like terms: 0 + 6.666666667 = 6.666666667 -8x + x2 = 6.666666667 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 6.666666667 + 16 Reorder the terms: 16 + -8x + x2 = 6.666666667 + 16 Combine like terms: 6.666666667 + 16 = 22.666666667 16 + -8x + x2 = 22.666666667 Factor a perfect square on the left side: (x + -4)(x + -4) = 22.666666667 Calculate the square root of the right side: 4.760952286 Break this problem into two subproblems by setting (x + -4) equal to 4.760952286 and -4.760952286.Subproblem 1
x + -4 = 4.760952286 Simplifying x + -4 = 4.760952286 Reorder the terms: -4 + x = 4.760952286 Solving -4 + x = 4.760952286 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 4.760952286 + 4 Combine like terms: -4 + 4 = 0 0 + x = 4.760952286 + 4 x = 4.760952286 + 4 Combine like terms: 4.760952286 + 4 = 8.760952286 x = 8.760952286 Simplifying x = 8.760952286Subproblem 2
x + -4 = -4.760952286 Simplifying x + -4 = -4.760952286 Reorder the terms: -4 + x = -4.760952286 Solving -4 + x = -4.760952286 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -4.760952286 + 4 Combine like terms: -4 + 4 = 0 0 + x = -4.760952286 + 4 x = -4.760952286 + 4 Combine like terms: -4.760952286 + 4 = -0.760952286 x = -0.760952286 Simplifying x = -0.760952286Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.760952286, -0.760952286}
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