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Simplifying 5x2 + -9x + 1 = 0 Reorder the terms: 1 + -9x + 5x2 = 0 Solving 1 + -9x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.2 + -1.8x + x2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + -1.8x + -0.2 + x2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + -1.8x + x2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + -1.8x + x2 = 0 + -0.2 -1.8x + x2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 -1.8x + x2 = -0.2 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 = -0.2 + 0.81 Reorder the terms: 0.81 + -1.8x + x2 = -0.2 + 0.81 Combine like terms: -0.2 + 0.81 = 0.61 0.81 + -1.8x + x2 = 0.61 Factor a perfect square on the left side: (x + -0.9)(x + -0.9) = 0.61 Calculate the square root of the right side: 0.781024968 Break this problem into two subproblems by setting (x + -0.9) equal to 0.781024968 and -0.781024968.Subproblem 1
x + -0.9 = 0.781024968 Simplifying x + -0.9 = 0.781024968 Reorder the terms: -0.9 + x = 0.781024968 Solving -0.9 + x = 0.781024968 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 = 0.781024968 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = 0.781024968 + 0.9 x = 0.781024968 + 0.9 Combine like terms: 0.781024968 + 0.9 = 1.681024968 x = 1.681024968 Simplifying x = 1.681024968Subproblem 2
x + -0.9 = -0.781024968 Simplifying x + -0.9 = -0.781024968 Reorder the terms: -0.9 + x = -0.781024968 Solving -0.9 + x = -0.781024968 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 = -0.781024968 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = -0.781024968 + 0.9 x = -0.781024968 + 0.9 Combine like terms: -0.781024968 + 0.9 = 0.118975032 x = 0.118975032 Simplifying x = 0.118975032Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.681024968, 0.118975032}
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