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Simplifying 10(10 + 18) = x(x + 3) Combine like terms: 10 + 18 = 28 10(28) = x(x + 3) Multiply 10 * 28 280 = x(x + 3) Reorder the terms: 280 = x(3 + x) 280 = (3 * x + x * x) 280 = (3x + x2) Solving 280 = 3x + x2 Solving for variable 'x'. Reorder the terms: 280 + -3x + -1x2 = 3x + -3x + x2 + -1x2 Combine like terms: 3x + -3x = 0 280 + -3x + -1x2 = 0 + x2 + -1x2 280 + -3x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 280 + -3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -280 + 3x + x2 = 0 Move the constant term to the right: Add '280' to each side of the equation. -280 + 3x + 280 + x2 = 0 + 280 Reorder the terms: -280 + 280 + 3x + x2 = 0 + 280 Combine like terms: -280 + 280 = 0 0 + 3x + x2 = 0 + 280 3x + x2 = 0 + 280 Combine like terms: 0 + 280 = 280 3x + x2 = 280 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 280 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 280 + 2.25 Combine like terms: 280 + 2.25 = 282.25 2.25 + 3x + x2 = 282.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 282.25 Calculate the square root of the right side: 16.800297616 Break this problem into two subproblems by setting (x + 1.5) equal to 16.800297616 and -16.800297616.Subproblem 1
x + 1.5 = 16.800297616 Simplifying x + 1.5 = 16.800297616 Reorder the terms: 1.5 + x = 16.800297616 Solving 1.5 + x = 16.800297616 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 16.800297616 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 16.800297616 + -1.5 x = 16.800297616 + -1.5 Combine like terms: 16.800297616 + -1.5 = 15.300297616 x = 15.300297616 Simplifying x = 15.300297616Subproblem 2
x + 1.5 = -16.800297616 Simplifying x + 1.5 = -16.800297616 Reorder the terms: 1.5 + x = -16.800297616 Solving 1.5 + x = -16.800297616 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -16.800297616 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -16.800297616 + -1.5 x = -16.800297616 + -1.5 Combine like terms: -16.800297616 + -1.5 = -18.300297616 x = -18.300297616 Simplifying x = -18.300297616Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.300297616, -18.300297616}
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