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Simplifying -7 + 10x(x + -5) + -3x = 4x + -3(18 + -1x) Reorder the terms: -7 + 10x(-5 + x) + -3x = 4x + -3(18 + -1x) -7 + (-5 * 10x + x * 10x) + -3x = 4x + -3(18 + -1x) -7 + (-50x + 10x2) + -3x = 4x + -3(18 + -1x) Reorder the terms: -7 + -50x + -3x + 10x2 = 4x + -3(18 + -1x) Combine like terms: -50x + -3x = -53x -7 + -53x + 10x2 = 4x + -3(18 + -1x) -7 + -53x + 10x2 = 4x + (18 * -3 + -1x * -3) -7 + -53x + 10x2 = 4x + (-54 + 3x) Reorder the terms: -7 + -53x + 10x2 = -54 + 4x + 3x Combine like terms: 4x + 3x = 7x -7 + -53x + 10x2 = -54 + 7x Solving -7 + -53x + 10x2 = -54 + 7x Solving for variable 'x'. Reorder the terms: -7 + 54 + -53x + -7x + 10x2 = -54 + 7x + 54 + -7x Combine like terms: -7 + 54 = 47 47 + -53x + -7x + 10x2 = -54 + 7x + 54 + -7x Combine like terms: -53x + -7x = -60x 47 + -60x + 10x2 = -54 + 7x + 54 + -7x Reorder the terms: 47 + -60x + 10x2 = -54 + 54 + 7x + -7x Combine like terms: -54 + 54 = 0 47 + -60x + 10x2 = 0 + 7x + -7x 47 + -60x + 10x2 = 7x + -7x Combine like terms: 7x + -7x = 0 47 + -60x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 4.7 + -6x + x2 = 0 Move the constant term to the right: Add '-4.7' to each side of the equation. 4.7 + -6x + -4.7 + x2 = 0 + -4.7 Reorder the terms: 4.7 + -4.7 + -6x + x2 = 0 + -4.7 Combine like terms: 4.7 + -4.7 = 0.0 0.0 + -6x + x2 = 0 + -4.7 -6x + x2 = 0 + -4.7 Combine like terms: 0 + -4.7 = -4.7 -6x + x2 = -4.7 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -4.7 + 9 Reorder the terms: 9 + -6x + x2 = -4.7 + 9 Combine like terms: -4.7 + 9 = 4.3 9 + -6x + x2 = 4.3 Factor a perfect square on the left side: (x + -3)(x + -3) = 4.3 Calculate the square root of the right side: 2.073644135 Break this problem into two subproblems by setting (x + -3) equal to 2.073644135 and -2.073644135.Subproblem 1
x + -3 = 2.073644135 Simplifying x + -3 = 2.073644135 Reorder the terms: -3 + x = 2.073644135 Solving -3 + x = 2.073644135 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 2.073644135 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.073644135 + 3 x = 2.073644135 + 3 Combine like terms: 2.073644135 + 3 = 5.073644135 x = 5.073644135 Simplifying x = 5.073644135Subproblem 2
x + -3 = -2.073644135 Simplifying x + -3 = -2.073644135 Reorder the terms: -3 + x = -2.073644135 Solving -3 + x = -2.073644135 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -2.073644135 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.073644135 + 3 x = -2.073644135 + 3 Combine like terms: -2.073644135 + 3 = 0.926355865 x = 0.926355865 Simplifying x = 0.926355865Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.073644135, 0.926355865}
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