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Simplifying 6x2 + 25x2 + -24x = 5 Reorder the terms: -24x + 6x2 + 25x2 = 5 Combine like terms: 6x2 + 25x2 = 31x2 -24x + 31x2 = 5 Solving -24x + 31x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + -24x + 31x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + -24x + 31x2 = 0 Begin completing the square. Divide all terms by 31 the coefficient of the squared term: Divide each side by '31'. -0.1612903226 + -0.7741935484x + x2 = 0 Move the constant term to the right: Add '0.1612903226' to each side of the equation. -0.1612903226 + -0.7741935484x + 0.1612903226 + x2 = 0 + 0.1612903226 Reorder the terms: -0.1612903226 + 0.1612903226 + -0.7741935484x + x2 = 0 + 0.1612903226 Combine like terms: -0.1612903226 + 0.1612903226 = 0.0000000000 0.0000000000 + -0.7741935484x + x2 = 0 + 0.1612903226 -0.7741935484x + x2 = 0 + 0.1612903226 Combine like terms: 0 + 0.1612903226 = 0.1612903226 -0.7741935484x + x2 = 0.1612903226 The x term is -0.7741935484x. Take half its coefficient (-0.3870967742). Square it (0.1498439126) and add it to both sides. Add '0.1498439126' to each side of the equation. -0.7741935484x + 0.1498439126 + x2 = 0.1612903226 + 0.1498439126 Reorder the terms: 0.1498439126 + -0.7741935484x + x2 = 0.1612903226 + 0.1498439126 Combine like terms: 0.1612903226 + 0.1498439126 = 0.3111342352 0.1498439126 + -0.7741935484x + x2 = 0.3111342352 Factor a perfect square on the left side: (x + -0.3870967742)(x + -0.3870967742) = 0.3111342352 Calculate the square root of the right side: 0.55779408 Break this problem into two subproblems by setting (x + -0.3870967742) equal to 0.55779408 and -0.55779408.Subproblem 1
x + -0.3870967742 = 0.55779408 Simplifying x + -0.3870967742 = 0.55779408 Reorder the terms: -0.3870967742 + x = 0.55779408 Solving -0.3870967742 + x = 0.55779408 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3870967742' to each side of the equation. -0.3870967742 + 0.3870967742 + x = 0.55779408 + 0.3870967742 Combine like terms: -0.3870967742 + 0.3870967742 = 0.0000000000 0.0000000000 + x = 0.55779408 + 0.3870967742 x = 0.55779408 + 0.3870967742 Combine like terms: 0.55779408 + 0.3870967742 = 0.9448908542 x = 0.9448908542 Simplifying x = 0.9448908542Subproblem 2
x + -0.3870967742 = -0.55779408 Simplifying x + -0.3870967742 = -0.55779408 Reorder the terms: -0.3870967742 + x = -0.55779408 Solving -0.3870967742 + x = -0.55779408 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3870967742' to each side of the equation. -0.3870967742 + 0.3870967742 + x = -0.55779408 + 0.3870967742 Combine like terms: -0.3870967742 + 0.3870967742 = 0.0000000000 0.0000000000 + x = -0.55779408 + 0.3870967742 x = -0.55779408 + 0.3870967742 Combine like terms: -0.55779408 + 0.3870967742 = -0.1706973058 x = -0.1706973058 Simplifying x = -0.1706973058Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9448908542, -0.1706973058}
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