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Simplifying 384 = (x + 10)(x + 10) Reorder the terms: 384 = (10 + x)(x + 10) Reorder the terms: 384 = (10 + x)(10 + x) Multiply (10 + x) * (10 + x) 384 = (10(10 + x) + x(10 + x)) 384 = ((10 * 10 + x * 10) + x(10 + x)) 384 = ((100 + 10x) + x(10 + x)) 384 = (100 + 10x + (10 * x + x * x)) 384 = (100 + 10x + (10x + x2)) Combine like terms: 10x + 10x = 20x 384 = (100 + 20x + x2) Solving 384 = 100 + 20x + x2 Solving for variable 'x'. Combine like terms: 384 + -100 = 284 284 + -20x + -1x2 = 100 + 20x + x2 + -100 + -20x + -1x2 Reorder the terms: 284 + -20x + -1x2 = 100 + -100 + 20x + -20x + x2 + -1x2 Combine like terms: 100 + -100 = 0 284 + -20x + -1x2 = 0 + 20x + -20x + x2 + -1x2 284 + -20x + -1x2 = 20x + -20x + x2 + -1x2 Combine like terms: 20x + -20x = 0 284 + -20x + -1x2 = 0 + x2 + -1x2 284 + -20x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 284 + -20x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -284 + 20x + x2 = 0 Move the constant term to the right: Add '284' to each side of the equation. -284 + 20x + 284 + x2 = 0 + 284 Reorder the terms: -284 + 284 + 20x + x2 = 0 + 284 Combine like terms: -284 + 284 = 0 0 + 20x + x2 = 0 + 284 20x + x2 = 0 + 284 Combine like terms: 0 + 284 = 284 20x + x2 = 284 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 284 + 100 Reorder the terms: 100 + 20x + x2 = 284 + 100 Combine like terms: 284 + 100 = 384 100 + 20x + x2 = 384 Factor a perfect square on the left side: (x + 10)(x + 10) = 384 Calculate the square root of the right side: 19.595917942 Break this problem into two subproblems by setting (x + 10) equal to 19.595917942 and -19.595917942.Subproblem 1
x + 10 = 19.595917942 Simplifying x + 10 = 19.595917942 Reorder the terms: 10 + x = 19.595917942 Solving 10 + x = 19.595917942 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 19.595917942 + -10 Combine like terms: 10 + -10 = 0 0 + x = 19.595917942 + -10 x = 19.595917942 + -10 Combine like terms: 19.595917942 + -10 = 9.595917942 x = 9.595917942 Simplifying x = 9.595917942Subproblem 2
x + 10 = -19.595917942 Simplifying x + 10 = -19.595917942 Reorder the terms: 10 + x = -19.595917942 Solving 10 + x = -19.595917942 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -19.595917942 + -10 Combine like terms: 10 + -10 = 0 0 + x = -19.595917942 + -10 x = -19.595917942 + -10 Combine like terms: -19.595917942 + -10 = -29.595917942 x = -29.595917942 Simplifying x = -29.595917942Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.595917942, -29.595917942}
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