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Simplifying 0.2x(x + 3) + -4(2x + -3) = 0.9 Reorder the terms: 0.2x(3 + x) + -4(2x + -3) = 0.9 (3 * 0.2x + x * 0.2x) + -4(2x + -3) = 0.9 (0.6x + 0.2x2) + -4(2x + -3) = 0.9 Reorder the terms: 0.6x + 0.2x2 + -4(-3 + 2x) = 0.9 0.6x + 0.2x2 + (-3 * -4 + 2x * -4) = 0.9 0.6x + 0.2x2 + (12 + -8x) = 0.9 Reorder the terms: 12 + 0.6x + -8x + 0.2x2 = 0.9 Combine like terms: 0.6x + -8x = -7.4x 12 + -7.4x + 0.2x2 = 0.9 Solving 12 + -7.4x + 0.2x2 = 0.9 Solving for variable 'x'. Reorder the terms: 12 + -0.9 + -7.4x + 0.2x2 = 0.9 + -0.9 Combine like terms: 12 + -0.9 = 11.1 11.1 + -7.4x + 0.2x2 = 0.9 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 11.1 + -7.4x + 0.2x2 = 0.0 Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. 55.5 + -37x + x2 = 0 Move the constant term to the right: Add '-55.5' to each side of the equation. 55.5 + -37x + -55.5 + x2 = 0 + -55.5 Reorder the terms: 55.5 + -55.5 + -37x + x2 = 0 + -55.5 Combine like terms: 55.5 + -55.5 = 0.0 0.0 + -37x + x2 = 0 + -55.5 -37x + x2 = 0 + -55.5 Combine like terms: 0 + -55.5 = -55.5 -37x + x2 = -55.5 The x term is -37x. Take half its coefficient (-18.5). Square it (342.25) and add it to both sides. Add '342.25' to each side of the equation. -37x + 342.25 + x2 = -55.5 + 342.25 Reorder the terms: 342.25 + -37x + x2 = -55.5 + 342.25 Combine like terms: -55.5 + 342.25 = 286.75 342.25 + -37x + x2 = 286.75 Factor a perfect square on the left side: (x + -18.5)(x + -18.5) = 286.75 Calculate the square root of the right side: 16.933694222 Break this problem into two subproblems by setting (x + -18.5) equal to 16.933694222 and -16.933694222.Subproblem 1
x + -18.5 = 16.933694222 Simplifying x + -18.5 = 16.933694222 Reorder the terms: -18.5 + x = 16.933694222 Solving -18.5 + x = 16.933694222 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.5' to each side of the equation. -18.5 + 18.5 + x = 16.933694222 + 18.5 Combine like terms: -18.5 + 18.5 = 0.0 0.0 + x = 16.933694222 + 18.5 x = 16.933694222 + 18.5 Combine like terms: 16.933694222 + 18.5 = 35.433694222 x = 35.433694222 Simplifying x = 35.433694222Subproblem 2
x + -18.5 = -16.933694222 Simplifying x + -18.5 = -16.933694222 Reorder the terms: -18.5 + x = -16.933694222 Solving -18.5 + x = -16.933694222 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.5' to each side of the equation. -18.5 + 18.5 + x = -16.933694222 + 18.5 Combine like terms: -18.5 + 18.5 = 0.0 0.0 + x = -16.933694222 + 18.5 x = -16.933694222 + 18.5 Combine like terms: -16.933694222 + 18.5 = 1.566305778 x = 1.566305778 Simplifying x = 1.566305778Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.433694222, 1.566305778}
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