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Simplifying 3.14x2 = 6x + 12.88 Reorder the terms: 3.14x2 = 12.88 + 6x Solving 3.14x2 = 12.88 + 6x Solving for variable 'x'. Reorder the terms: -12.88 + -6x + 3.14x2 = 12.88 + 6x + -12.88 + -6x Reorder the terms: -12.88 + -6x + 3.14x2 = 12.88 + -12.88 + 6x + -6x Combine like terms: 12.88 + -12.88 = 0.00 -12.88 + -6x + 3.14x2 = 0.00 + 6x + -6x -12.88 + -6x + 3.14x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -12.88 + -6x + 3.14x2 = 0 Begin completing the square. Divide all terms by 3.14 the coefficient of the squared term: Divide each side by '3.14'. -4.101910828 + -1.910828025x + x2 = 0 Move the constant term to the right: Add '4.101910828' to each side of the equation. -4.101910828 + -1.910828025x + 4.101910828 + x2 = 0 + 4.101910828 Reorder the terms: -4.101910828 + 4.101910828 + -1.910828025x + x2 = 0 + 4.101910828 Combine like terms: -4.101910828 + 4.101910828 = 0.000000000 0.000000000 + -1.910828025x + x2 = 0 + 4.101910828 -1.910828025x + x2 = 0 + 4.101910828 Combine like terms: 0 + 4.101910828 = 4.101910828 -1.910828025x + x2 = 4.101910828 The x term is -1.910828025x. Take half its coefficient (-0.9554140125). Square it (0.9128159353) and add it to both sides. Add '0.9128159353' to each side of the equation. -1.910828025x + 0.9128159353 + x2 = 4.101910828 + 0.9128159353 Reorder the terms: 0.9128159353 + -1.910828025x + x2 = 4.101910828 + 0.9128159353 Combine like terms: 4.101910828 + 0.9128159353 = 5.0147267633 0.9128159353 + -1.910828025x + x2 = 5.0147267633 Factor a perfect square on the left side: (x + -0.9554140125)(x + -0.9554140125) = 5.0147267633 Calculate the square root of the right side: 2.239358561 Break this problem into two subproblems by setting (x + -0.9554140125) equal to 2.239358561 and -2.239358561.Subproblem 1
x + -0.9554140125 = 2.239358561 Simplifying x + -0.9554140125 = 2.239358561 Reorder the terms: -0.9554140125 + x = 2.239358561 Solving -0.9554140125 + x = 2.239358561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9554140125' to each side of the equation. -0.9554140125 + 0.9554140125 + x = 2.239358561 + 0.9554140125 Combine like terms: -0.9554140125 + 0.9554140125 = 0.0000000000 0.0000000000 + x = 2.239358561 + 0.9554140125 x = 2.239358561 + 0.9554140125 Combine like terms: 2.239358561 + 0.9554140125 = 3.1947725735 x = 3.1947725735 Simplifying x = 3.1947725735Subproblem 2
x + -0.9554140125 = -2.239358561 Simplifying x + -0.9554140125 = -2.239358561 Reorder the terms: -0.9554140125 + x = -2.239358561 Solving -0.9554140125 + x = -2.239358561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9554140125' to each side of the equation. -0.9554140125 + 0.9554140125 + x = -2.239358561 + 0.9554140125 Combine like terms: -0.9554140125 + 0.9554140125 = 0.0000000000 0.0000000000 + x = -2.239358561 + 0.9554140125 x = -2.239358561 + 0.9554140125 Combine like terms: -2.239358561 + 0.9554140125 = -1.2839445485 x = -1.2839445485 Simplifying x = -1.2839445485Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.1947725735, -1.2839445485}
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