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Simplifying -0.45x2 + 0.9x + 5 = 0 Reorder the terms: 5 + 0.9x + -0.45x2 = 0 Solving 5 + 0.9x + -0.45x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.45 the coefficient of the squared term: Divide each side by '-0.45'. -11.11111111 + -2x + x2 = 0 Move the constant term to the right: Add '11.11111111' to each side of the equation. -11.11111111 + -2x + 11.11111111 + x2 = 0 + 11.11111111 Reorder the terms: -11.11111111 + 11.11111111 + -2x + x2 = 0 + 11.11111111 Combine like terms: -11.11111111 + 11.11111111 = 0.00000000 0.00000000 + -2x + x2 = 0 + 11.11111111 -2x + x2 = 0 + 11.11111111 Combine like terms: 0 + 11.11111111 = 11.11111111 -2x + x2 = 11.11111111 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 11.11111111 + 1 Reorder the terms: 1 + -2x + x2 = 11.11111111 + 1 Combine like terms: 11.11111111 + 1 = 12.11111111 1 + -2x + x2 = 12.11111111 Factor a perfect square on the left side: (x + -1)(x + -1) = 12.11111111 Calculate the square root of the right side: 3.480102169 Break this problem into two subproblems by setting (x + -1) equal to 3.480102169 and -3.480102169.Subproblem 1
x + -1 = 3.480102169 Simplifying x + -1 = 3.480102169 Reorder the terms: -1 + x = 3.480102169 Solving -1 + x = 3.480102169 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 3.480102169 + 1 Combine like terms: -1 + 1 = 0 0 + x = 3.480102169 + 1 x = 3.480102169 + 1 Combine like terms: 3.480102169 + 1 = 4.480102169 x = 4.480102169 Simplifying x = 4.480102169Subproblem 2
x + -1 = -3.480102169 Simplifying x + -1 = -3.480102169 Reorder the terms: -1 + x = -3.480102169 Solving -1 + x = -3.480102169 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -3.480102169 + 1 Combine like terms: -1 + 1 = 0 0 + x = -3.480102169 + 1 x = -3.480102169 + 1 Combine like terms: -3.480102169 + 1 = -2.480102169 x = -2.480102169 Simplifying x = -2.480102169Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.480102169, -2.480102169}
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