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Simplifying 10x(x + 10) = 3x + 52 Reorder the terms: 10x(10 + x) = 3x + 52 (10 * 10x + x * 10x) = 3x + 52 (100x + 10x2) = 3x + 52 Reorder the terms: 100x + 10x2 = 52 + 3x Solving 100x + 10x2 = 52 + 3x Solving for variable 'x'. Reorder the terms: -52 + 100x + -3x + 10x2 = 52 + 3x + -52 + -3x Combine like terms: 100x + -3x = 97x -52 + 97x + 10x2 = 52 + 3x + -52 + -3x Reorder the terms: -52 + 97x + 10x2 = 52 + -52 + 3x + -3x Combine like terms: 52 + -52 = 0 -52 + 97x + 10x2 = 0 + 3x + -3x -52 + 97x + 10x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -52 + 97x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -5.2 + 9.7x + x2 = 0 Move the constant term to the right: Add '5.2' to each side of the equation. -5.2 + 9.7x + 5.2 + x2 = 0 + 5.2 Reorder the terms: -5.2 + 5.2 + 9.7x + x2 = 0 + 5.2 Combine like terms: -5.2 + 5.2 = 0.0 0.0 + 9.7x + x2 = 0 + 5.2 9.7x + x2 = 0 + 5.2 Combine like terms: 0 + 5.2 = 5.2 9.7x + x2 = 5.2 The x term is 9.7x. Take half its coefficient (4.85). Square it (23.5225) and add it to both sides. Add '23.5225' to each side of the equation. 9.7x + 23.5225 + x2 = 5.2 + 23.5225 Reorder the terms: 23.5225 + 9.7x + x2 = 5.2 + 23.5225 Combine like terms: 5.2 + 23.5225 = 28.7225 23.5225 + 9.7x + x2 = 28.7225 Factor a perfect square on the left side: (x + 4.85)(x + 4.85) = 28.7225 Calculate the square root of the right side: 5.359337646 Break this problem into two subproblems by setting (x + 4.85) equal to 5.359337646 and -5.359337646.Subproblem 1
x + 4.85 = 5.359337646 Simplifying x + 4.85 = 5.359337646 Reorder the terms: 4.85 + x = 5.359337646 Solving 4.85 + x = 5.359337646 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.85' to each side of the equation. 4.85 + -4.85 + x = 5.359337646 + -4.85 Combine like terms: 4.85 + -4.85 = 0.00 0.00 + x = 5.359337646 + -4.85 x = 5.359337646 + -4.85 Combine like terms: 5.359337646 + -4.85 = 0.509337646 x = 0.509337646 Simplifying x = 0.509337646Subproblem 2
x + 4.85 = -5.359337646 Simplifying x + 4.85 = -5.359337646 Reorder the terms: 4.85 + x = -5.359337646 Solving 4.85 + x = -5.359337646 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.85' to each side of the equation. 4.85 + -4.85 + x = -5.359337646 + -4.85 Combine like terms: 4.85 + -4.85 = 0.00 0.00 + x = -5.359337646 + -4.85 x = -5.359337646 + -4.85 Combine like terms: -5.359337646 + -4.85 = -10.209337646 x = -10.209337646 Simplifying x = -10.209337646Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.509337646, -10.209337646}
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