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Simplifying 5x2 + -4x + 1 = 225 Reorder the terms: 1 + -4x + 5x2 = 225 Solving 1 + -4x + 5x2 = 225 Solving for variable 'x'. Reorder the terms: 1 + -225 + -4x + 5x2 = 225 + -225 Combine like terms: 1 + -225 = -224 -224 + -4x + 5x2 = 225 + -225 Combine like terms: 225 + -225 = 0 -224 + -4x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -44.8 + -0.8x + x2 = 0 Move the constant term to the right: Add '44.8' to each side of the equation. -44.8 + -0.8x + 44.8 + x2 = 0 + 44.8 Reorder the terms: -44.8 + 44.8 + -0.8x + x2 = 0 + 44.8 Combine like terms: -44.8 + 44.8 = 0.0 0.0 + -0.8x + x2 = 0 + 44.8 -0.8x + x2 = 0 + 44.8 Combine like terms: 0 + 44.8 = 44.8 -0.8x + x2 = 44.8 The x term is -0.8x. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8x + 0.16 + x2 = 44.8 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = 44.8 + 0.16 Combine like terms: 44.8 + 0.16 = 44.96 0.16 + -0.8x + x2 = 44.96 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = 44.96 Calculate the square root of the right side: 6.705221846 Break this problem into two subproblems by setting (x + -0.4) equal to 6.705221846 and -6.705221846.Subproblem 1
x + -0.4 = 6.705221846 Simplifying x + -0.4 = 6.705221846 Reorder the terms: -0.4 + x = 6.705221846 Solving -0.4 + x = 6.705221846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = 6.705221846 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 6.705221846 + 0.4 x = 6.705221846 + 0.4 Combine like terms: 6.705221846 + 0.4 = 7.105221846 x = 7.105221846 Simplifying x = 7.105221846Subproblem 2
x + -0.4 = -6.705221846 Simplifying x + -0.4 = -6.705221846 Reorder the terms: -0.4 + x = -6.705221846 Solving -0.4 + x = -6.705221846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = -6.705221846 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -6.705221846 + 0.4 x = -6.705221846 + 0.4 Combine like terms: -6.705221846 + 0.4 = -6.305221846 x = -6.305221846 Simplifying x = -6.305221846Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.105221846, -6.305221846}
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