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Simplifying 7x2 + 10 = 4x + 12 Reorder the terms: 10 + 7x2 = 4x + 12 Reorder the terms: 10 + 7x2 = 12 + 4x Solving 10 + 7x2 = 12 + 4x Solving for variable 'x'. Reorder the terms: 10 + -12 + -4x + 7x2 = 12 + 4x + -12 + -4x Combine like terms: 10 + -12 = -2 -2 + -4x + 7x2 = 12 + 4x + -12 + -4x Reorder the terms: -2 + -4x + 7x2 = 12 + -12 + 4x + -4x Combine like terms: 12 + -12 = 0 -2 + -4x + 7x2 = 0 + 4x + -4x -2 + -4x + 7x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -2 + -4x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.2857142857 + -0.5714285714x + x2 = 0 Move the constant term to the right: Add '0.2857142857' to each side of the equation. -0.2857142857 + -0.5714285714x + 0.2857142857 + x2 = 0 + 0.2857142857 Reorder the terms: -0.2857142857 + 0.2857142857 + -0.5714285714x + x2 = 0 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + -0.5714285714x + x2 = 0 + 0.2857142857 -0.5714285714x + x2 = 0 + 0.2857142857 Combine like terms: 0 + 0.2857142857 = 0.2857142857 -0.5714285714x + x2 = 0.2857142857 The x term is -0.5714285714x. Take half its coefficient (-0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. -0.5714285714x + 0.08163265305 + x2 = 0.2857142857 + 0.08163265305 Reorder the terms: 0.08163265305 + -0.5714285714x + x2 = 0.2857142857 + 0.08163265305 Combine like terms: 0.2857142857 + 0.08163265305 = 0.36734693875 0.08163265305 + -0.5714285714x + x2 = 0.36734693875 Factor a perfect square on the left side: (x + -0.2857142857)(x + -0.2857142857) = 0.36734693875 Calculate the square root of the right side: 0.606091527 Break this problem into two subproblems by setting (x + -0.2857142857) equal to 0.606091527 and -0.606091527.Subproblem 1
x + -0.2857142857 = 0.606091527 Simplifying x + -0.2857142857 = 0.606091527 Reorder the terms: -0.2857142857 + x = 0.606091527 Solving -0.2857142857 + x = 0.606091527 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + x = 0.606091527 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = 0.606091527 + 0.2857142857 x = 0.606091527 + 0.2857142857 Combine like terms: 0.606091527 + 0.2857142857 = 0.8918058127 x = 0.8918058127 Simplifying x = 0.8918058127Subproblem 2
x + -0.2857142857 = -0.606091527 Simplifying x + -0.2857142857 = -0.606091527 Reorder the terms: -0.2857142857 + x = -0.606091527 Solving -0.2857142857 + x = -0.606091527 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + x = -0.606091527 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = -0.606091527 + 0.2857142857 x = -0.606091527 + 0.2857142857 Combine like terms: -0.606091527 + 0.2857142857 = -0.3203772413 x = -0.3203772413 Simplifying x = -0.3203772413Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8918058127, -0.3203772413}
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