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Simplifying 692 = x2 + 5x Reorder the terms: 692 = 5x + x2 Solving 692 = 5x + x2 Solving for variable 'x'. Reorder the terms: 692 + -5x + -1x2 = 5x + -5x + x2 + -1x2 Combine like terms: 5x + -5x = 0 692 + -5x + -1x2 = 0 + x2 + -1x2 692 + -5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 692 + -5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -692 + 5x + x2 = 0 Move the constant term to the right: Add '692' to each side of the equation. -692 + 5x + 692 + x2 = 0 + 692 Reorder the terms: -692 + 692 + 5x + x2 = 0 + 692 Combine like terms: -692 + 692 = 0 0 + 5x + x2 = 0 + 692 5x + x2 = 0 + 692 Combine like terms: 0 + 692 = 692 5x + x2 = 692 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 692 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 692 + 6.25 Combine like terms: 692 + 6.25 = 698.25 6.25 + 5x + x2 = 698.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 698.25 Calculate the square root of the right side: 26.424420523 Break this problem into two subproblems by setting (x + 2.5) equal to 26.424420523 and -26.424420523.Subproblem 1
x + 2.5 = 26.424420523 Simplifying x + 2.5 = 26.424420523 Reorder the terms: 2.5 + x = 26.424420523 Solving 2.5 + x = 26.424420523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 26.424420523 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 26.424420523 + -2.5 x = 26.424420523 + -2.5 Combine like terms: 26.424420523 + -2.5 = 23.924420523 x = 23.924420523 Simplifying x = 23.924420523Subproblem 2
x + 2.5 = -26.424420523 Simplifying x + 2.5 = -26.424420523 Reorder the terms: 2.5 + x = -26.424420523 Solving 2.5 + x = -26.424420523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -26.424420523 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -26.424420523 + -2.5 x = -26.424420523 + -2.5 Combine like terms: -26.424420523 + -2.5 = -28.924420523 x = -28.924420523 Simplifying x = -28.924420523Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.924420523, -28.924420523}
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