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Simplifying x(3 + x) + -4(2x + 3) = 7049 (3 * x + x * x) + -4(2x + 3) = 7049 (3x + x2) + -4(2x + 3) = 7049 Reorder the terms: 3x + x2 + -4(3 + 2x) = 7049 3x + x2 + (3 * -4 + 2x * -4) = 7049 3x + x2 + (-12 + -8x) = 7049 Reorder the terms: -12 + 3x + -8x + x2 = 7049 Combine like terms: 3x + -8x = -5x -12 + -5x + x2 = 7049 Solving -12 + -5x + x2 = 7049 Solving for variable 'x'. Reorder the terms: -12 + -7049 + -5x + x2 = 7049 + -7049 Combine like terms: -12 + -7049 = -7061 -7061 + -5x + x2 = 7049 + -7049 Combine like terms: 7049 + -7049 = 0 -7061 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '7061' to each side of the equation. -7061 + -5x + 7061 + x2 = 0 + 7061 Reorder the terms: -7061 + 7061 + -5x + x2 = 0 + 7061 Combine like terms: -7061 + 7061 = 0 0 + -5x + x2 = 0 + 7061 -5x + x2 = 0 + 7061 Combine like terms: 0 + 7061 = 7061 -5x + x2 = 7061 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 = 7061 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 7061 + 6.25 Combine like terms: 7061 + 6.25 = 7067.25 6.25 + -5x + x2 = 7067.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 7067.25 Calculate the square root of the right side: 84.066937615 Break this problem into two subproblems by setting (x + -2.5) equal to 84.066937615 and -84.066937615.Subproblem 1
x + -2.5 = 84.066937615 Simplifying x + -2.5 = 84.066937615 Reorder the terms: -2.5 + x = 84.066937615 Solving -2.5 + x = 84.066937615 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 = 84.066937615 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 84.066937615 + 2.5 x = 84.066937615 + 2.5 Combine like terms: 84.066937615 + 2.5 = 86.566937615 x = 86.566937615 Simplifying x = 86.566937615Subproblem 2
x + -2.5 = -84.066937615 Simplifying x + -2.5 = -84.066937615 Reorder the terms: -2.5 + x = -84.066937615 Solving -2.5 + x = -84.066937615 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 = -84.066937615 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -84.066937615 + 2.5 x = -84.066937615 + 2.5 Combine like terms: -84.066937615 + 2.5 = -81.566937615 x = -81.566937615 Simplifying x = -81.566937615Solution
The solution to the problem is based on the solutions from the subproblems. x = {86.566937615, -81.566937615}
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