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Simplifying 8a2 = -71a + -90 Reorder the terms: 8a2 = -90 + -71a Solving 8a2 = -90 + -71a Solving for variable 'a'. Reorder the terms: 90 + 71a + 8a2 = -90 + -71a + 90 + 71a Reorder the terms: 90 + 71a + 8a2 = -90 + 90 + -71a + 71a Combine like terms: -90 + 90 = 0 90 + 71a + 8a2 = 0 + -71a + 71a 90 + 71a + 8a2 = -71a + 71a Combine like terms: -71a + 71a = 0 90 + 71a + 8a2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 11.25 + 8.875a + a2 = 0 Move the constant term to the right: Add '-11.25' to each side of the equation. 11.25 + 8.875a + -11.25 + a2 = 0 + -11.25 Reorder the terms: 11.25 + -11.25 + 8.875a + a2 = 0 + -11.25 Combine like terms: 11.25 + -11.25 = 0.00 0.00 + 8.875a + a2 = 0 + -11.25 8.875a + a2 = 0 + -11.25 Combine like terms: 0 + -11.25 = -11.25 8.875a + a2 = -11.25 The a term is 8.875a. Take half its coefficient (4.4375). Square it (19.69140625) and add it to both sides. Add '19.69140625' to each side of the equation. 8.875a + 19.69140625 + a2 = -11.25 + 19.69140625 Reorder the terms: 19.69140625 + 8.875a + a2 = -11.25 + 19.69140625 Combine like terms: -11.25 + 19.69140625 = 8.44140625 19.69140625 + 8.875a + a2 = 8.44140625 Factor a perfect square on the left side: (a + 4.4375)(a + 4.4375) = 8.44140625 Calculate the square root of the right side: 2.905409825 Break this problem into two subproblems by setting (a + 4.4375) equal to 2.905409825 and -2.905409825.Subproblem 1
a + 4.4375 = 2.905409825 Simplifying a + 4.4375 = 2.905409825 Reorder the terms: 4.4375 + a = 2.905409825 Solving 4.4375 + a = 2.905409825 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4.4375' to each side of the equation. 4.4375 + -4.4375 + a = 2.905409825 + -4.4375 Combine like terms: 4.4375 + -4.4375 = 0.0000 0.0000 + a = 2.905409825 + -4.4375 a = 2.905409825 + -4.4375 Combine like terms: 2.905409825 + -4.4375 = -1.532090175 a = -1.532090175 Simplifying a = -1.532090175Subproblem 2
a + 4.4375 = -2.905409825 Simplifying a + 4.4375 = -2.905409825 Reorder the terms: 4.4375 + a = -2.905409825 Solving 4.4375 + a = -2.905409825 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4.4375' to each side of the equation. 4.4375 + -4.4375 + a = -2.905409825 + -4.4375 Combine like terms: 4.4375 + -4.4375 = 0.0000 0.0000 + a = -2.905409825 + -4.4375 a = -2.905409825 + -4.4375 Combine like terms: -2.905409825 + -4.4375 = -7.342909825 a = -7.342909825 Simplifying a = -7.342909825Solution
The solution to the problem is based on the solutions from the subproblems. a = {-1.532090175, -7.342909825}
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