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Simplifying 6x + 14.84 = 3.14(x * x) Reorder the terms: 14.84 + 6x = 3.14(x * x) Multiply x * x 14.84 + 6x = 3.14(x2) Solving 14.84 + 6x = 3.14x2 Solving for variable 'x'. Combine like terms: 3.14x2 + -3.14x2 = 0.00 14.84 + 6x + -3.14x2 = 0.00 Begin completing the square. Divide all terms by -3.14 the coefficient of the squared term: Divide each side by '-3.14'. -4.72611465 + -1.910828025x + x2 = 0 Move the constant term to the right: Add '4.72611465' to each side of the equation. -4.72611465 + -1.910828025x + 4.72611465 + x2 = 0 + 4.72611465 Reorder the terms: -4.72611465 + 4.72611465 + -1.910828025x + x2 = 0 + 4.72611465 Combine like terms: -4.72611465 + 4.72611465 = 0.00000000 0.00000000 + -1.910828025x + x2 = 0 + 4.72611465 -1.910828025x + x2 = 0 + 4.72611465 Combine like terms: 0 + 4.72611465 = 4.72611465 -1.910828025x + x2 = 4.72611465 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 = 4.72611465 + 0.9128159353 Reorder the terms: 0.9128159353 + -1.910828025x + x2 = 4.72611465 + 0.9128159353 Combine like terms: 4.72611465 + 0.9128159353 = 5.6389305853 0.9128159353 + -1.910828025x + x2 = 5.6389305853 Factor a perfect square on the left side: (x + -0.9554140125)(x + -0.9554140125) = 5.6389305853 Calculate the square root of the right side: 2.374643254 Break this problem into two subproblems by setting (x + -0.9554140125) equal to 2.374643254 and -2.374643254.Subproblem 1
x + -0.9554140125 = 2.374643254 Simplifying x + -0.9554140125 = 2.374643254 Reorder the terms: -0.9554140125 + x = 2.374643254 Solving -0.9554140125 + x = 2.374643254 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 = 2.374643254 + 0.9554140125 Combine like terms: -0.9554140125 + 0.9554140125 = 0.0000000000 0.0000000000 + x = 2.374643254 + 0.9554140125 x = 2.374643254 + 0.9554140125 Combine like terms: 2.374643254 + 0.9554140125 = 3.3300572665 x = 3.3300572665 Simplifying x = 3.3300572665Subproblem 2
x + -0.9554140125 = -2.374643254 Simplifying x + -0.9554140125 = -2.374643254 Reorder the terms: -0.9554140125 + x = -2.374643254 Solving -0.9554140125 + x = -2.374643254 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 = -2.374643254 + 0.9554140125 Combine like terms: -0.9554140125 + 0.9554140125 = 0.0000000000 0.0000000000 + x = -2.374643254 + 0.9554140125 x = -2.374643254 + 0.9554140125 Combine like terms: -2.374643254 + 0.9554140125 = -1.4192292415 x = -1.4192292415 Simplifying x = -1.4192292415Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.3300572665, -1.4192292415}
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