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Simplifying 5x + 50 = x + 1.25x2 Reorder the terms: 50 + 5x = x + 1.25x2 Solving 50 + 5x = x + 1.25x2 Solving for variable 'x'. Combine like terms: 5x + -1x = 4x 50 + 4x + -1.25x2 = x + 1.25x2 + -1x + -1.25x2 Reorder the terms: 50 + 4x + -1.25x2 = x + -1x + 1.25x2 + -1.25x2 Combine like terms: x + -1x = 0 50 + 4x + -1.25x2 = 0 + 1.25x2 + -1.25x2 50 + 4x + -1.25x2 = 1.25x2 + -1.25x2 Combine like terms: 1.25x2 + -1.25x2 = 0.00 50 + 4x + -1.25x2 = 0.00 Begin completing the square. Divide all terms by -1.25 the coefficient of the squared term: Divide each side by '-1.25'. -40 + -3.2x + x2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + -3.2x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + -3.2x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -3.2x + x2 = 0 + 40 -3.2x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 -3.2x + x2 = 40 The x term is -3.2x. Take half its coefficient (-1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. -3.2x + 2.56 + x2 = 40 + 2.56 Reorder the terms: 2.56 + -3.2x + x2 = 40 + 2.56 Combine like terms: 40 + 2.56 = 42.56 2.56 + -3.2x + x2 = 42.56 Factor a perfect square on the left side: (x + -1.6)(x + -1.6) = 42.56 Calculate the square root of the right side: 6.523802572 Break this problem into two subproblems by setting (x + -1.6) equal to 6.523802572 and -6.523802572.Subproblem 1
x + -1.6 = 6.523802572 Simplifying x + -1.6 = 6.523802572 Reorder the terms: -1.6 + x = 6.523802572 Solving -1.6 + x = 6.523802572 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + x = 6.523802572 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = 6.523802572 + 1.6 x = 6.523802572 + 1.6 Combine like terms: 6.523802572 + 1.6 = 8.123802572 x = 8.123802572 Simplifying x = 8.123802572Subproblem 2
x + -1.6 = -6.523802572 Simplifying x + -1.6 = -6.523802572 Reorder the terms: -1.6 + x = -6.523802572 Solving -1.6 + x = -6.523802572 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + x = -6.523802572 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = -6.523802572 + 1.6 x = -6.523802572 + 1.6 Combine like terms: -6.523802572 + 1.6 = -4.923802572 x = -4.923802572 Simplifying x = -4.923802572Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.123802572, -4.923802572}
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