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Simplifying 4x2 + 6x + -10 = x2 + 6 Reorder the terms: -10 + 6x + 4x2 = x2 + 6 Reorder the terms: -10 + 6x + 4x2 = 6 + x2 Solving -10 + 6x + 4x2 = 6 + x2 Solving for variable 'x'. Reorder the terms: -10 + -6 + 6x + 4x2 + -1x2 = 6 + x2 + -6 + -1x2 Combine like terms: -10 + -6 = -16 -16 + 6x + 4x2 + -1x2 = 6 + x2 + -6 + -1x2 Combine like terms: 4x2 + -1x2 = 3x2 -16 + 6x + 3x2 = 6 + x2 + -6 + -1x2 Reorder the terms: -16 + 6x + 3x2 = 6 + -6 + x2 + -1x2 Combine like terms: 6 + -6 = 0 -16 + 6x + 3x2 = 0 + x2 + -1x2 -16 + 6x + 3x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -16 + 6x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -5.333333333 + 2x + x2 = 0 Move the constant term to the right: Add '5.333333333' to each side of the equation. -5.333333333 + 2x + 5.333333333 + x2 = 0 + 5.333333333 Reorder the terms: -5.333333333 + 5.333333333 + 2x + x2 = 0 + 5.333333333 Combine like terms: -5.333333333 + 5.333333333 = 0.000000000 0.000000000 + 2x + x2 = 0 + 5.333333333 2x + x2 = 0 + 5.333333333 Combine like terms: 0 + 5.333333333 = 5.333333333 2x + x2 = 5.333333333 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 5.333333333 + 1 Reorder the terms: 1 + 2x + x2 = 5.333333333 + 1 Combine like terms: 5.333333333 + 1 = 6.333333333 1 + 2x + x2 = 6.333333333 Factor a perfect square on the left side: (x + 1)(x + 1) = 6.333333333 Calculate the square root of the right side: 2.516611478 Break this problem into two subproblems by setting (x + 1) equal to 2.516611478 and -2.516611478.Subproblem 1
x + 1 = 2.516611478 Simplifying x + 1 = 2.516611478 Reorder the terms: 1 + x = 2.516611478 Solving 1 + x = 2.516611478 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 2.516611478 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.516611478 + -1 x = 2.516611478 + -1 Combine like terms: 2.516611478 + -1 = 1.516611478 x = 1.516611478 Simplifying x = 1.516611478Subproblem 2
x + 1 = -2.516611478 Simplifying x + 1 = -2.516611478 Reorder the terms: 1 + x = -2.516611478 Solving 1 + x = -2.516611478 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -2.516611478 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.516611478 + -1 x = -2.516611478 + -1 Combine like terms: -2.516611478 + -1 = -3.516611478 x = -3.516611478 Simplifying x = -3.516611478Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.516611478, -3.516611478}
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