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Simplifying 7x2 + -6x + -13x = 4 Reorder the terms: -6x + -13x + 7x2 = 4 Combine like terms: -6x + -13x = -19x -19x + 7x2 = 4 Solving -19x + 7x2 = 4 Solving for variable 'x'. Reorder the terms: -4 + -19x + 7x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + -19x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.5714285714 + -2.714285714x + x2 = 0 Move the constant term to the right: Add '0.5714285714' to each side of the equation. -0.5714285714 + -2.714285714x + 0.5714285714 + x2 = 0 + 0.5714285714 Reorder the terms: -0.5714285714 + 0.5714285714 + -2.714285714x + x2 = 0 + 0.5714285714 Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000 0.0000000000 + -2.714285714x + x2 = 0 + 0.5714285714 -2.714285714x + x2 = 0 + 0.5714285714 Combine like terms: 0 + 0.5714285714 = 0.5714285714 -2.714285714x + x2 = 0.5714285714 The x term is -2.714285714x. Take half its coefficient (-1.357142857). Square it (1.841836734) and add it to both sides. Add '1.841836734' to each side of the equation. -2.714285714x + 1.841836734 + x2 = 0.5714285714 + 1.841836734 Reorder the terms: 1.841836734 + -2.714285714x + x2 = 0.5714285714 + 1.841836734 Combine like terms: 0.5714285714 + 1.841836734 = 2.4132653054 1.841836734 + -2.714285714x + x2 = 2.4132653054 Factor a perfect square on the left side: (x + -1.357142857)(x + -1.357142857) = 2.4132653054 Calculate the square root of the right side: 1.553468798 Break this problem into two subproblems by setting (x + -1.357142857) equal to 1.553468798 and -1.553468798.Subproblem 1
x + -1.357142857 = 1.553468798 Simplifying x + -1.357142857 = 1.553468798 Reorder the terms: -1.357142857 + x = 1.553468798 Solving -1.357142857 + x = 1.553468798 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.357142857' to each side of the equation. -1.357142857 + 1.357142857 + x = 1.553468798 + 1.357142857 Combine like terms: -1.357142857 + 1.357142857 = 0.000000000 0.000000000 + x = 1.553468798 + 1.357142857 x = 1.553468798 + 1.357142857 Combine like terms: 1.553468798 + 1.357142857 = 2.910611655 x = 2.910611655 Simplifying x = 2.910611655Subproblem 2
x + -1.357142857 = -1.553468798 Simplifying x + -1.357142857 = -1.553468798 Reorder the terms: -1.357142857 + x = -1.553468798 Solving -1.357142857 + x = -1.553468798 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.357142857' to each side of the equation. -1.357142857 + 1.357142857 + x = -1.553468798 + 1.357142857 Combine like terms: -1.357142857 + 1.357142857 = 0.000000000 0.000000000 + x = -1.553468798 + 1.357142857 x = -1.553468798 + 1.357142857 Combine like terms: -1.553468798 + 1.357142857 = -0.196325941 x = -0.196325941 Simplifying x = -0.196325941Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.910611655, -0.196325941}
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