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Simplifying -0.4(x + -1.5)(x + -1.5) + 2 = -10 Reorder the terms: -0.4(-1.5 + x)(x + -1.5) + 2 = -10 Reorder the terms: -0.4(-1.5 + x)(-1.5 + x) + 2 = -10 Multiply (-1.5 + x) * (-1.5 + x) -0.4(-1.5(-1.5 + x) + x(-1.5 + x)) + 2 = -10 -0.4((-1.5 * -1.5 + x * -1.5) + x(-1.5 + x)) + 2 = -10 -0.4((2.25 + -1.5x) + x(-1.5 + x)) + 2 = -10 -0.4(2.25 + -1.5x + (-1.5 * x + x * x)) + 2 = -10 -0.4(2.25 + -1.5x + (-1.5x + x2)) + 2 = -10 Combine like terms: -1.5x + -1.5x = -3x -0.4(2.25 + -3x + x2) + 2 = -10 (2.25 * -0.4 + -3x * -0.4 + x2 * -0.4) + 2 = -10 (-0.9 + 1.2x + -0.4x2) + 2 = -10 Reorder the terms: -0.9 + 2 + 1.2x + -0.4x2 = -10 Combine like terms: -0.9 + 2 = 1.1 1.1 + 1.2x + -0.4x2 = -10 Solving 1.1 + 1.2x + -0.4x2 = -10 Solving for variable 'x'. Reorder the terms: 1.1 + 10 + 1.2x + -0.4x2 = -10 + 10 Combine like terms: 1.1 + 10 = 11.1 11.1 + 1.2x + -0.4x2 = -10 + 10 Combine like terms: -10 + 10 = 0 11.1 + 1.2x + -0.4x2 = 0 Begin completing the square. Divide all terms by -0.4 the coefficient of the squared term: Divide each side by '-0.4'. -27.75 + -3x + x2 = 0 Move the constant term to the right: Add '27.75' to each side of the equation. -27.75 + -3x + 27.75 + x2 = 0 + 27.75 Reorder the terms: -27.75 + 27.75 + -3x + x2 = 0 + 27.75 Combine like terms: -27.75 + 27.75 = 0.00 0.00 + -3x + x2 = 0 + 27.75 -3x + x2 = 0 + 27.75 Combine like terms: 0 + 27.75 = 27.75 -3x + x2 = 27.75 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 27.75 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 27.75 + 2.25 Combine like terms: 27.75 + 2.25 = 30 2.25 + -3x + x2 = 30 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 30 Calculate the square root of the right side: 5.477225575 Break this problem into two subproblems by setting (x + -1.5) equal to 5.477225575 and -5.477225575.Subproblem 1
x + -1.5 = 5.477225575 Simplifying x + -1.5 = 5.477225575 Reorder the terms: -1.5 + x = 5.477225575 Solving -1.5 + x = 5.477225575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 5.477225575 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 5.477225575 + 1.5 x = 5.477225575 + 1.5 Combine like terms: 5.477225575 + 1.5 = 6.977225575 x = 6.977225575 Simplifying x = 6.977225575Subproblem 2
x + -1.5 = -5.477225575 Simplifying x + -1.5 = -5.477225575 Reorder the terms: -1.5 + x = -5.477225575 Solving -1.5 + x = -5.477225575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -5.477225575 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -5.477225575 + 1.5 x = -5.477225575 + 1.5 Combine like terms: -5.477225575 + 1.5 = -3.977225575 x = -3.977225575 Simplifying x = -3.977225575Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.977225575, -3.977225575}
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