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Simplifying x2 * 3.14 = 6x + 13.16 Reorder the terms for easier multiplication: 3.14x2 = 6x + 13.16 Reorder the terms: 3.14x2 = 13.16 + 6x Solving 3.14x2 = 13.16 + 6x Solving for variable 'x'. Reorder the terms: -13.16 + -6x + 3.14x2 = 13.16 + 6x + -13.16 + -6x Reorder the terms: -13.16 + -6x + 3.14x2 = 13.16 + -13.16 + 6x + -6x Combine like terms: 13.16 + -13.16 = 0.00 -13.16 + -6x + 3.14x2 = 0.00 + 6x + -6x -13.16 + -6x + 3.14x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -13.16 + -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'. -4.191082803 + -1.910828025x + x2 = 0 Move the constant term to the right: Add '4.191082803' to each side of the equation. -4.191082803 + -1.910828025x + 4.191082803 + x2 = 0 + 4.191082803 Reorder the terms: -4.191082803 + 4.191082803 + -1.910828025x + x2 = 0 + 4.191082803 Combine like terms: -4.191082803 + 4.191082803 = 0.000000000 0.000000000 + -1.910828025x + x2 = 0 + 4.191082803 -1.910828025x + x2 = 0 + 4.191082803 Combine like terms: 0 + 4.191082803 = 4.191082803 -1.910828025x + x2 = 4.191082803 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 = 4.191082803 + 0.9128159353 Reorder the terms: 0.9128159353 + -1.910828025x + x2 = 4.191082803 + 0.9128159353 Combine like terms: 4.191082803 + 0.9128159353 = 5.1038987383 0.9128159353 + -1.910828025x + x2 = 5.1038987383 Factor a perfect square on the left side: (x + -0.9554140125)(x + -0.9554140125) = 5.1038987383 Calculate the square root of the right side: 2.259180988 Break this problem into two subproblems by setting (x + -0.9554140125) equal to 2.259180988 and -2.259180988.Subproblem 1
x + -0.9554140125 = 2.259180988 Simplifying x + -0.9554140125 = 2.259180988 Reorder the terms: -0.9554140125 + x = 2.259180988 Solving -0.9554140125 + x = 2.259180988 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 = 2.259180988 + 0.9554140125 Combine like terms: -0.9554140125 + 0.9554140125 = 0.0000000000 0.0000000000 + x = 2.259180988 + 0.9554140125 x = 2.259180988 + 0.9554140125 Combine like terms: 2.259180988 + 0.9554140125 = 3.2145950005 x = 3.2145950005 Simplifying x = 3.2145950005Subproblem 2
x + -0.9554140125 = -2.259180988 Simplifying x + -0.9554140125 = -2.259180988 Reorder the terms: -0.9554140125 + x = -2.259180988 Solving -0.9554140125 + x = -2.259180988 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 = -2.259180988 + 0.9554140125 Combine like terms: -0.9554140125 + 0.9554140125 = 0.0000000000 0.0000000000 + x = -2.259180988 + 0.9554140125 x = -2.259180988 + 0.9554140125 Combine like terms: -2.259180988 + 0.9554140125 = -1.3037669755 x = -1.3037669755 Simplifying x = -1.3037669755Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.2145950005, -1.3037669755}
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