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Simplifying (3x)(42x + 1) = 6x + 2 Remove parenthesis around (3x) 3x(42x + 1) = 6x + 2 Reorder the terms: 3x(1 + 42x) = 6x + 2 (1 * 3x + 42x * 3x) = 6x + 2 (3x + 126x2) = 6x + 2 Reorder the terms: 3x + 126x2 = 2 + 6x Solving 3x + 126x2 = 2 + 6x Solving for variable 'x'. Reorder the terms: -2 + 3x + -6x + 126x2 = 2 + 6x + -2 + -6x Combine like terms: 3x + -6x = -3x -2 + -3x + 126x2 = 2 + 6x + -2 + -6x Reorder the terms: -2 + -3x + 126x2 = 2 + -2 + 6x + -6x Combine like terms: 2 + -2 = 0 -2 + -3x + 126x2 = 0 + 6x + -6x -2 + -3x + 126x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -2 + -3x + 126x2 = 0 Begin completing the square. Divide all terms by 126 the coefficient of the squared term: Divide each side by '126'. -0.01587301587 + -0.02380952381x + x2 = 0 Move the constant term to the right: Add '0.01587301587' to each side of the equation. -0.01587301587 + -0.02380952381x + 0.01587301587 + x2 = 0 + 0.01587301587 Reorder the terms: -0.01587301587 + 0.01587301587 + -0.02380952381x + x2 = 0 + 0.01587301587 Combine like terms: -0.01587301587 + 0.01587301587 = 0.00000000000 0.00000000000 + -0.02380952381x + x2 = 0 + 0.01587301587 -0.02380952381x + x2 = 0 + 0.01587301587 Combine like terms: 0 + 0.01587301587 = 0.01587301587 -0.02380952381x + x2 = 0.01587301587 The x term is -0.02380952381x. Take half its coefficient (-0.01190476191). Square it (0.0001417233561) and add it to both sides. Add '0.0001417233561' to each side of the equation. -0.02380952381x + 0.0001417233561 + x2 = 0.01587301587 + 0.0001417233561 Reorder the terms: 0.0001417233561 + -0.02380952381x + x2 = 0.01587301587 + 0.0001417233561 Combine like terms: 0.01587301587 + 0.0001417233561 = 0.0160147392261 0.0001417233561 + -0.02380952381x + x2 = 0.0160147392261 Factor a perfect square on the left side: (x + -0.01190476191)(x + -0.01190476191) = 0.0160147392261 Calculate the square root of the right side: 0.126549355 Break this problem into two subproblems by setting (x + -0.01190476191) equal to 0.126549355 and -0.126549355.Subproblem 1
x + -0.01190476191 = 0.126549355 Simplifying x + -0.01190476191 = 0.126549355 Reorder the terms: -0.01190476191 + x = 0.126549355 Solving -0.01190476191 + x = 0.126549355 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.01190476191' to each side of the equation. -0.01190476191 + 0.01190476191 + x = 0.126549355 + 0.01190476191 Combine like terms: -0.01190476191 + 0.01190476191 = 0.00000000000 0.00000000000 + x = 0.126549355 + 0.01190476191 x = 0.126549355 + 0.01190476191 Combine like terms: 0.126549355 + 0.01190476191 = 0.13845411691 x = 0.13845411691 Simplifying x = 0.13845411691Subproblem 2
x + -0.01190476191 = -0.126549355 Simplifying x + -0.01190476191 = -0.126549355 Reorder the terms: -0.01190476191 + x = -0.126549355 Solving -0.01190476191 + x = -0.126549355 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.01190476191' to each side of the equation. -0.01190476191 + 0.01190476191 + x = -0.126549355 + 0.01190476191 Combine like terms: -0.01190476191 + 0.01190476191 = 0.00000000000 0.00000000000 + x = -0.126549355 + 0.01190476191 x = -0.126549355 + 0.01190476191 Combine like terms: -0.126549355 + 0.01190476191 = -0.11464459309 x = -0.11464459309 Simplifying x = -0.11464459309Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.13845411691, -0.11464459309}
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