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Simplifying 5x2 + -9x = 0.4 Reorder the terms: -9x + 5x2 = 0.4 Solving -9x + 5x2 = 0.4 Solving for variable 'x'. Reorder the terms: -0.4 + -9x + 5x2 = 0.4 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 -0.4 + -9x + 5x2 = 0.0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.08 + -1.8x + x2 = 0.0 Move the constant term to the right: Add '0.08' to each side of the equation. -0.08 + -1.8x + 0.08 + x2 = 0.0 + 0.08 Reorder the terms: -0.08 + 0.08 + -1.8x + x2 = 0.0 + 0.08 Combine like terms: -0.08 + 0.08 = 0.00 0.00 + -1.8x + x2 = 0.0 + 0.08 -1.8x + x2 = 0.0 + 0.08 Combine like terms: 0.0 + 0.08 = 0.08 -1.8x + x2 = 0.08 The x term is -1.8x. Take half its coefficient (-0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. -1.8x + 0.81 + x2 = 0.08 + 0.81 Reorder the terms: 0.81 + -1.8x + x2 = 0.08 + 0.81 Combine like terms: 0.08 + 0.81 = 0.89 0.81 + -1.8x + x2 = 0.89 Factor a perfect square on the left side: (x + -0.9)(x + -0.9) = 0.89 Calculate the square root of the right side: 0.943398113 Break this problem into two subproblems by setting (x + -0.9) equal to 0.943398113 and -0.943398113.Subproblem 1
x + -0.9 = 0.943398113 Simplifying x + -0.9 = 0.943398113 Reorder the terms: -0.9 + x = 0.943398113 Solving -0.9 + x = 0.943398113 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + x = 0.943398113 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = 0.943398113 + 0.9 x = 0.943398113 + 0.9 Combine like terms: 0.943398113 + 0.9 = 1.843398113 x = 1.843398113 Simplifying x = 1.843398113Subproblem 2
x + -0.9 = -0.943398113 Simplifying x + -0.9 = -0.943398113 Reorder the terms: -0.9 + x = -0.943398113 Solving -0.9 + x = -0.943398113 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + x = -0.943398113 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = -0.943398113 + 0.9 x = -0.943398113 + 0.9 Combine like terms: -0.943398113 + 0.9 = -0.043398113 x = -0.043398113 Simplifying x = -0.043398113Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.843398113, -0.043398113}
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