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Simplifying 2470 = (x + 15)(x + -10) Reorder the terms: 2470 = (15 + x)(x + -10) Reorder the terms: 2470 = (15 + x)(-10 + x) Multiply (15 + x) * (-10 + x) 2470 = (15(-10 + x) + x(-10 + x)) 2470 = ((-10 * 15 + x * 15) + x(-10 + x)) 2470 = ((-150 + 15x) + x(-10 + x)) 2470 = (-150 + 15x + (-10 * x + x * x)) 2470 = (-150 + 15x + (-10x + x2)) Combine like terms: 15x + -10x = 5x 2470 = (-150 + 5x + x2) Solving 2470 = -150 + 5x + x2 Solving for variable 'x'. Combine like terms: 2470 + 150 = 2620 2620 + -5x + -1x2 = -150 + 5x + x2 + 150 + -5x + -1x2 Reorder the terms: 2620 + -5x + -1x2 = -150 + 150 + 5x + -5x + x2 + -1x2 Combine like terms: -150 + 150 = 0 2620 + -5x + -1x2 = 0 + 5x + -5x + x2 + -1x2 2620 + -5x + -1x2 = 5x + -5x + x2 + -1x2 Combine like terms: 5x + -5x = 0 2620 + -5x + -1x2 = 0 + x2 + -1x2 2620 + -5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 2620 + -5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2620 + 5x + x2 = 0 Move the constant term to the right: Add '2620' to each side of the equation. -2620 + 5x + 2620 + x2 = 0 + 2620 Reorder the terms: -2620 + 2620 + 5x + x2 = 0 + 2620 Combine like terms: -2620 + 2620 = 0 0 + 5x + x2 = 0 + 2620 5x + x2 = 0 + 2620 Combine like terms: 0 + 2620 = 2620 5x + x2 = 2620 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 = 2620 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 2620 + 6.25 Combine like terms: 2620 + 6.25 = 2626.25 6.25 + 5x + x2 = 2626.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 2626.25 Calculate the square root of the right side: 51.246951129 Break this problem into two subproblems by setting (x + 2.5) equal to 51.246951129 and -51.246951129.Subproblem 1
x + 2.5 = 51.246951129 Simplifying x + 2.5 = 51.246951129 Reorder the terms: 2.5 + x = 51.246951129 Solving 2.5 + x = 51.246951129 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 = 51.246951129 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 51.246951129 + -2.5 x = 51.246951129 + -2.5 Combine like terms: 51.246951129 + -2.5 = 48.746951129 x = 48.746951129 Simplifying x = 48.746951129Subproblem 2
x + 2.5 = -51.246951129 Simplifying x + 2.5 = -51.246951129 Reorder the terms: 2.5 + x = -51.246951129 Solving 2.5 + x = -51.246951129 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 = -51.246951129 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -51.246951129 + -2.5 x = -51.246951129 + -2.5 Combine like terms: -51.246951129 + -2.5 = -53.746951129 x = -53.746951129 Simplifying x = -53.746951129Solution
The solution to the problem is based on the solutions from the subproblems. x = {48.746951129, -53.746951129}
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