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Simplifying 0.45 = x * x + 2x + -5 Multiply x * x 0.45 = x2 + 2x + -5 Reorder the terms: 0.45 = -5 + 2x + x2 Solving 0.45 = -5 + 2x + x2 Solving for variable 'x'. Combine like terms: 0.45 + 5 = 5.45 5.45 + -2x + -1x2 = -5 + 2x + x2 + 5 + -2x + -1x2 Reorder the terms: 5.45 + -2x + -1x2 = -5 + 5 + 2x + -2x + x2 + -1x2 Combine like terms: -5 + 5 = 0 5.45 + -2x + -1x2 = 0 + 2x + -2x + x2 + -1x2 5.45 + -2x + -1x2 = 2x + -2x + x2 + -1x2 Combine like terms: 2x + -2x = 0 5.45 + -2x + -1x2 = 0 + x2 + -1x2 5.45 + -2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 5.45 + -2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -5.45 + 2x + x2 = 0 Move the constant term to the right: Add '5.45' to each side of the equation. -5.45 + 2x + 5.45 + x2 = 0 + 5.45 Reorder the terms: -5.45 + 5.45 + 2x + x2 = 0 + 5.45 Combine like terms: -5.45 + 5.45 = 0.00 0.00 + 2x + x2 = 0 + 5.45 2x + x2 = 0 + 5.45 Combine like terms: 0 + 5.45 = 5.45 2x + x2 = 5.45 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 = 5.45 + 1 Reorder the terms: 1 + 2x + x2 = 5.45 + 1 Combine like terms: 5.45 + 1 = 6.45 1 + 2x + x2 = 6.45 Factor a perfect square on the left side: (x + 1)(x + 1) = 6.45 Calculate the square root of the right side: 2.53968502 Break this problem into two subproblems by setting (x + 1) equal to 2.53968502 and -2.53968502.Subproblem 1
x + 1 = 2.53968502 Simplifying x + 1 = 2.53968502 Reorder the terms: 1 + x = 2.53968502 Solving 1 + x = 2.53968502 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 = 2.53968502 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.53968502 + -1 x = 2.53968502 + -1 Combine like terms: 2.53968502 + -1 = 1.53968502 x = 1.53968502 Simplifying x = 1.53968502Subproblem 2
x + 1 = -2.53968502 Simplifying x + 1 = -2.53968502 Reorder the terms: 1 + x = -2.53968502 Solving 1 + x = -2.53968502 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 = -2.53968502 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.53968502 + -1 x = -2.53968502 + -1 Combine like terms: -2.53968502 + -1 = -3.53968502 x = -3.53968502 Simplifying x = -3.53968502Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.53968502, -3.53968502}
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