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Simplifying 24 * 42 = -48 + 4x + x2 Multiply 24 * 42 1008 = -48 + 4x + x2 Solving 1008 = -48 + 4x + x2 Solving for variable 'x'. Combine like terms: 1008 + 48 = 1056 1056 + -4x + -1x2 = -48 + 4x + x2 + 48 + -4x + -1x2 Reorder the terms: 1056 + -4x + -1x2 = -48 + 48 + 4x + -4x + x2 + -1x2 Combine like terms: -48 + 48 = 0 1056 + -4x + -1x2 = 0 + 4x + -4x + x2 + -1x2 1056 + -4x + -1x2 = 4x + -4x + x2 + -1x2 Combine like terms: 4x + -4x = 0 1056 + -4x + -1x2 = 0 + x2 + -1x2 1056 + -4x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 1056 + -4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1056 + 4x + x2 = 0 Move the constant term to the right: Add '1056' to each side of the equation. -1056 + 4x + 1056 + x2 = 0 + 1056 Reorder the terms: -1056 + 1056 + 4x + x2 = 0 + 1056 Combine like terms: -1056 + 1056 = 0 0 + 4x + x2 = 0 + 1056 4x + x2 = 0 + 1056 Combine like terms: 0 + 1056 = 1056 4x + x2 = 1056 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 1056 + 4 Reorder the terms: 4 + 4x + x2 = 1056 + 4 Combine like terms: 1056 + 4 = 1060 4 + 4x + x2 = 1060 Factor a perfect square on the left side: (x + 2)(x + 2) = 1060 Calculate the square root of the right side: 32.557641192 Break this problem into two subproblems by setting (x + 2) equal to 32.557641192 and -32.557641192.Subproblem 1
x + 2 = 32.557641192 Simplifying x + 2 = 32.557641192 Reorder the terms: 2 + x = 32.557641192 Solving 2 + x = 32.557641192 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 32.557641192 + -2 Combine like terms: 2 + -2 = 0 0 + x = 32.557641192 + -2 x = 32.557641192 + -2 Combine like terms: 32.557641192 + -2 = 30.557641192 x = 30.557641192 Simplifying x = 30.557641192Subproblem 2
x + 2 = -32.557641192 Simplifying x + 2 = -32.557641192 Reorder the terms: 2 + x = -32.557641192 Solving 2 + x = -32.557641192 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -32.557641192 + -2 Combine like terms: 2 + -2 = 0 0 + x = -32.557641192 + -2 x = -32.557641192 + -2 Combine like terms: -32.557641192 + -2 = -34.557641192 x = -34.557641192 Simplifying x = -34.557641192Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.557641192, -34.557641192}
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