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Simplifying 8x2 + 19x = 6 Reorder the terms: 19x + 8x2 = 6 Solving 19x + 8x2 = 6 Solving for variable 'x'. Reorder the terms: -6 + 19x + 8x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + 19x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.75 + 2.375x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + 2.375x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + 2.375x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + 2.375x + x2 = 0 + 0.75 2.375x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 2.375x + x2 = 0.75 The x term is 2.375x. Take half its coefficient (1.1875). Square it (1.41015625) and add it to both sides. Add '1.41015625' to each side of the equation. 2.375x + 1.41015625 + x2 = 0.75 + 1.41015625 Reorder the terms: 1.41015625 + 2.375x + x2 = 0.75 + 1.41015625 Combine like terms: 0.75 + 1.41015625 = 2.16015625 1.41015625 + 2.375x + x2 = 2.16015625 Factor a perfect square on the left side: (x + 1.1875)(x + 1.1875) = 2.16015625 Calculate the square root of the right side: 1.469747002 Break this problem into two subproblems by setting (x + 1.1875) equal to 1.469747002 and -1.469747002.Subproblem 1
x + 1.1875 = 1.469747002 Simplifying x + 1.1875 = 1.469747002 Reorder the terms: 1.1875 + x = 1.469747002 Solving 1.1875 + x = 1.469747002 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1875' to each side of the equation. 1.1875 + -1.1875 + x = 1.469747002 + -1.1875 Combine like terms: 1.1875 + -1.1875 = 0.0000 0.0000 + x = 1.469747002 + -1.1875 x = 1.469747002 + -1.1875 Combine like terms: 1.469747002 + -1.1875 = 0.282247002 x = 0.282247002 Simplifying x = 0.282247002Subproblem 2
x + 1.1875 = -1.469747002 Simplifying x + 1.1875 = -1.469747002 Reorder the terms: 1.1875 + x = -1.469747002 Solving 1.1875 + x = -1.469747002 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1875' to each side of the equation. 1.1875 + -1.1875 + x = -1.469747002 + -1.1875 Combine like terms: 1.1875 + -1.1875 = 0.0000 0.0000 + x = -1.469747002 + -1.1875 x = -1.469747002 + -1.1875 Combine like terms: -1.469747002 + -1.1875 = -2.657247002 x = -2.657247002 Simplifying x = -2.657247002Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.282247002, -2.657247002}
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